diff --git a/src/calibre/gui2/__init__.py b/src/calibre/gui2/__init__.py
index a1dbfe5398..47262bbaa7 100644
--- a/src/calibre/gui2/__init__.py
+++ b/src/calibre/gui2/__init__.py
@@ -10,8 +10,8 @@ import sys
 import threading
 from contextlib import contextmanager
 from qt.core import (
-    QT_VERSION, QApplication, QBuffer, QByteArray, QColor, QCoreApplication,
-    QDateTime, QDesktopServices, QDialog, QDialogButtonBox, QEvent, QFileDialog,
+    QT_VERSION, QApplication, QBuffer, QByteArray, QColor, QDateTime,
+    QDesktopServices, QDialog, QDialogButtonBox, QEvent, QFileDialog,
     QFileIconProvider, QFileInfo, QFont, QFontDatabase, QFontInfo, QFontMetrics,
     QGuiApplication, QIcon, QIODevice, QLocale, QNetworkProxyFactory, QObject,
     QPalette, QSettings, QSocketNotifier, QStringListModel, QStyle, Qt, QThread,
@@ -381,8 +381,8 @@ def min_available_height():
 
 
 def get_screen_dpi():
-    d = QApplication.desktop()
-    return (d.logicalDpiX(), d.logicalDpiY())
+    s = QApplication.instance().primaryScreen()
+    return s.logicalDotsPerInchX(), s.logicalDotsPerInchY()
 
 
 _is_widescreen = None
@@ -820,8 +820,7 @@ class ResizableDialog(QDialog):
     def __init__(self, *args, **kwargs):
         QDialog.__init__(self, *args)
         self.setupUi(self)
-        desktop = QCoreApplication.instance().desktop()
-        geom = desktop.availableGeometry(self)
+        geom = self.screen().availableSize()
         nh, nw = max(550, geom.height()-25), max(700, geom.width()-10)
         nh = min(self.height(), nh)
         nw = min(self.width(), nw)
@@ -1049,7 +1048,7 @@ class Application(QApplication):
         return restored
 
     def ensure_window_on_screen(self, widget):
-        screen_rect = self.desktop().availableGeometry(widget)
+        screen_rect = widget.screen().availableGeometry()
         g = widget.geometry()
         w = min(screen_rect.width(), g.width())
         h = min(screen_rect.height(), g.height())
diff --git a/src/calibre/gui2/library/delegates.py b/src/calibre/gui2/library/delegates.py
index f6230b978f..c2a0cfe039 100644
--- a/src/calibre/gui2/library/delegates.py
+++ b/src/calibre/gui2/library/delegates.py
@@ -775,7 +775,7 @@ class CcTemplateDelegate(QStyledItemDelegate):  # {{{
         editor = TemplateDialog(parent, text, mi)
         editor.setWindowTitle(_("Edit template"))
         editor.textbox.setTabChangesFocus(False)
-        editor.textbox.setTabStopWidth(20)
+        editor.textbox.setTabStopDistance(20)
         d = editor.exec()
         if d:
             m.setData(index, (editor.rule[1]), Qt.ItemDataRole.EditRole)
diff --git a/src/calibre/gui2/preferences/template_functions.py b/src/calibre/gui2/preferences/template_functions.py
index cded4db9da..b0708947e0 100644
--- a/src/calibre/gui2/preferences/template_functions.py
+++ b/src/calibre/gui2/preferences/template_functions.py
@@ -181,7 +181,7 @@ class ConfigWidget(ConfigWidgetBase, Ui_Form):
         self.replace_button.setEnabled(False)
         self.clear_button.clicked.connect(self.clear_button_clicked)
         self.replace_button.clicked.connect(self.replace_button_clicked)
-        self.program.setTabStopWidth(20)
+        self.program.setTabStopDistance(20)
         self.highlighter = PythonHighlighter(self.program.document())
 
         self.te_textbox = self.template_editor.textbox
diff --git a/src/calibre/gui2/preferences/template_functions.ui b/src/calibre/gui2/preferences/template_functions.ui
index 72a45d988c..f68144a369 100644
--- a/src/calibre/gui2/preferences/template_functions.ui
+++ b/src/calibre/gui2/preferences/template_functions.ui
@@ -237,7 +237,7 @@
            <property name="documentTitle">
             <string notr="true"/>
            </property>
-           <property name="tabStopWidth">
+           <property name="tabStopDistance">
             <number>30</number>
            </property>
           </widget>
diff --git a/src/calibre/gui2/tweak_book/diff/view.py b/src/calibre/gui2/tweak_book/diff/view.py
index 0e099ab16f..0580f30a9e 100644
--- a/src/calibre/gui2/tweak_book/diff/view.py
+++ b/src/calibre/gui2/tweak_book/diff/view.py
@@ -117,7 +117,7 @@ class TextBrowser(PlainTextEdit):  # {{{
         font.setPointSizeF(tprefs['editor_font_size'])
         self.setFont(font)
         self.calculate_metrics()
-        self.setTabStopWidth(tprefs['editor_tab_stop_width'] * self.space_width)
+        self.setTabStopDistance(tprefs['editor_tab_stop_width'] * self.space_width)
         font = self.heading_font = QFont(self.font())
         font.setPointSizeF(tprefs['editor_font_size'] * 1.5)
         font.setBold(True)
diff --git a/src/calibre/gui2/tweak_book/editor/insert_resource.py b/src/calibre/gui2/tweak_book/editor/insert_resource.py
index 4c517791ee..3a82b7e451 100644
--- a/src/calibre/gui2/tweak_book/editor/insert_resource.py
+++ b/src/calibre/gui2/tweak_book/editor/insert_resource.py
@@ -226,7 +226,7 @@ class InsertImage(Dialog):
         self.fm = fm = QSortFilterProxyModel(self.view)
         self.fm.setDynamicSortFilter(self.for_browsing)
         fm.setSourceModel(self.model)
-        fm.setFilterCaseSensitivity(False)
+        fm.setFilterCaseSensitivity(Qt.CaseSensitivity.CaseInsensitive)
         v.setModel(fm)
         l.addWidget(v, 1, 0, 1, 2)
         v.pressed.connect(self.pressed)
diff --git a/src/calibre/gui2/tweak_book/editor/text.py b/src/calibre/gui2/tweak_book/editor/text.py
index ad51f01d71..b95ba71c82 100644
--- a/src/calibre/gui2/tweak_book/editor/text.py
+++ b/src/calibre/gui2/tweak_book/editor/text.py
@@ -224,10 +224,10 @@ class TextEdit(PlainTextEdit):
         self.setLineWrapMode(QPlainTextEdit.LineWrapMode.WidgetWidth if prefs['editor_line_wrap'] else QPlainTextEdit.LineWrapMode.NoWrap)
         theme = get_theme(prefs['editor_theme'])
         self.apply_theme(theme)
-        w = self.fontMetrics()
-        self.space_width = w.width(' ')
+        fm = self.fontMetrics()
+        self.space_width = fm.horizontalAdvance(' ')
         self.tw = self.smarts.override_tab_stop_width if self.smarts.override_tab_stop_width is not None else prefs['editor_tab_stop_width']
-        self.setTabStopWidth(self.tw * self.space_width)
+        self.setTabStopDistance(self.tw * self.space_width)
         if dictionaries_changed:
             self.highlighter.rehighlight()
 
@@ -258,9 +258,9 @@ class TextEdit(PlainTextEdit):
         self.tooltip_font.setPointSizeF(font.pointSizeF() - 1.)
         self.setFont(font)
         self.highlighter.apply_theme(theme)
-        w = self.fontMetrics()
-        self.number_width = max(map(lambda x:w.width(str(x)), range(10)))
-        self.size_hint = QSize(self.expected_geometry[0] * w.averageCharWidth(), self.expected_geometry[1] * w.height())
+        fm = self.fontMetrics()
+        self.number_width = max(map(lambda x:fm.horizontalAdvance(str(x)), range(10)))
+        self.size_hint = QSize(self.expected_geometry[0] * fm.averageCharWidth(), self.expected_geometry[1] * fm.height())
         self.highlight_color = theme_color(theme, 'HighlightRegion', 'bg')
         self.highlight_cursor_line()
         self.completion_popup.clear_caches(), self.completion_popup.update()
@@ -276,7 +276,7 @@ class TextEdit(PlainTextEdit):
             self.smarts = sclass(self)
             if self.smarts.override_tab_stop_width is not None:
                 self.tw = self.smarts.override_tab_stop_width
-                self.setTabStopWidth(self.tw * self.space_width)
+                self.setTabStopDistance(self.tw * self.space_width)
         if isinstance(text, bytes):
             text = text.decode('utf-8', 'replace')
         self.setPlainText(unicodedata.normalize('NFC', str(text)))
diff --git a/src/calibre/gui2/tweak_book/preview.py b/src/calibre/gui2/tweak_book/preview.py
index cfdf0113cc..49f6897b25 100644
--- a/src/calibre/gui2/tweak_book/preview.py
+++ b/src/calibre/gui2/tweak_book/preview.py
@@ -12,9 +12,9 @@ from qt.core import (
     pyqtSignal
 )
 from qt.webengine import (
-    QWebEngineContextMenuData, QWebEnginePage, QWebEngineProfile, QWebEngineScript,
-    QWebEngineSettings, QWebEngineUrlRequestJob, QWebEngineUrlSchemeHandler,
-    QWebEngineView
+    QWebEngineContextMenuRequest, QWebEnginePage, QWebEngineProfile,
+    QWebEngineScript, QWebEngineSettings, QWebEngineUrlRequestJob,
+    QWebEngineUrlSchemeHandler, QWebEngineView
 )
 from threading import Thread
 
@@ -33,13 +33,12 @@ from calibre.gui2.palette import dark_color, dark_link_color, dark_text_color
 from calibre.gui2.tweak_book import TOP, actions, current_container, editors, tprefs
 from calibre.gui2.tweak_book.file_list import OpenWithHandler
 from calibre.gui2.viewer.web_view import handle_mathjax_request, send_reply
-from calibre.utils.webengine import (
-    Bridge, create_script, from_js, insert_scripts,
-    secure_webengine, to_js
-)
 from calibre.gui2.webengine import RestartingWebEngineView
 from calibre.gui2.widgets2 import HistoryLineEdit2
 from calibre.utils.ipc.simple_worker import offload_worker
+from calibre.utils.webengine import (
+    Bridge, create_script, from_js, insert_scripts, secure_webengine, to_js
+)
 from polyglot.builtins import iteritems
 from polyglot.queue import Empty, Queue
 from polyglot.urllib import urlparse
@@ -462,7 +461,7 @@ class WebView(RestartingWebEngineView, OpenWithHandler):
 
     def contextMenuEvent(self, ev):
         menu = QMenu(self)
-        data = self._page.contextMenuData()
+        data = self.lastContextMenuRequest()
         url = data.linkUrl()
         url = str(url.toString(NO_URL_FORMATTING)).strip()
         text = data.selectedText()
@@ -474,7 +473,7 @@ class WebView(RestartingWebEngineView, OpenWithHandler):
         menu.addAction(QIcon(I('debug.png')), _('Inspect element'), self.inspect)
         if url.partition(':')[0].lower() in {'http', 'https'}:
             menu.addAction(_('Open link'), partial(safe_open_url, data.linkUrl()))
-        if QWebEngineContextMenuData.MediaType.MediaTypeImage <= data.mediaType() <= QWebEngineContextMenuData.MediaType.MediaTypeFile:
+        if QWebEngineContextMenuRequest.MediaType.MediaTypeImage.value <= data.mediaType().value <= QWebEngineContextMenuRequest.MediaType.MediaTypeFile.value:
             url = data.mediaUrl()
             if url.scheme() == FAKE_PROTOCOL:
                 href = url.path().lstrip('/')
@@ -483,7 +482,7 @@ class WebView(RestartingWebEngineView, OpenWithHandler):
                     resource_name = c.href_to_name(href)
                     if resource_name and c.exists(resource_name) and resource_name not in c.names_that_must_not_be_changed:
                         self.add_open_with_actions(menu, resource_name)
-                        if data.mediaType() == QWebEngineContextMenuData.MediaType.MediaTypeImage:
+                        if data.mediaType() == QWebEngineContextMenuRequest.MediaType.MediaTypeImage:
                             mime = c.mime_map[resource_name]
                             if mime.startswith('image/'):
                                 menu.addAction(_('Edit %s') % resource_name, partial(self.edit_image, resource_name))
diff --git a/src/calibre/gui2/tweak_book/ui.py b/src/calibre/gui2/tweak_book/ui.py
index 3377b6d006..6742049a45 100644
--- a/src/calibre/gui2/tweak_book/ui.py
+++ b/src/calibre/gui2/tweak_book/ui.py
@@ -385,8 +385,8 @@ class Main(MainWindow):
         for v, h in product(('top', 'bottom'), ('left', 'right')):
             p = f'dock_{v}_{h}'
             pref = tprefs[p] or tprefs.defaults[p]
-            area = getattr(Qt, '%sDockWidgetArea' % capitalize({'vertical':h, 'horizontal':v}[pref]))
-            self.setCorner(getattr(Qt, '%s%sCorner' % tuple(map(capitalize, (v, h)))), area)
+            area = getattr(Qt.DockWidgetArea, '%sDockWidgetArea' % capitalize({'vertical':h, 'horizontal':v}[pref]))
+            self.setCorner(getattr(Qt.Corner, '%s%sCorner' % tuple(map(capitalize, (v, h)))), area)
         self.preview.apply_settings()
         self.live_css.apply_theme()
         for bar in (self.global_bar, self.tools_bar, self.plugins_bar):
diff --git a/src/calibre/gui2/viewer/web_view.py b/src/calibre/gui2/viewer/web_view.py
index 104bf7b055..ad504d8cff 100644
--- a/src/calibre/gui2/viewer/web_view.py
+++ b/src/calibre/gui2/viewer/web_view.py
@@ -314,7 +314,7 @@ def apply_font_settings(page_or_view):
     else:
         s.resetFontFamily(QWebEngineSettings.FontFamily.SansSerifFont)
     sf = fs.get('standard_font') or 'serif'
-    sf = getattr(s, {'serif': 'SerifFont', 'sans': 'SansSerifFont', 'mono': 'FixedFont'}[sf])
+    sf = getattr(QWebEngineSettings.FontFamily, {'serif': 'SerifFont', 'sans': 'SansSerifFont', 'mono': 'FixedFont'}[sf])
     s.setFontFamily(QWebEngineSettings.FontFamily.StandardFont, s.fontFamily(sf))
     old_minimum = s.fontSize(QWebEngineSettings.FontSize.MinimumFontSize)
     old_base = s.fontSize(QWebEngineSettings.FontSize.DefaultFontSize)
diff --git a/src/calibre/gui2/widgets2.py b/src/calibre/gui2/widgets2.py
index 89f35e79d2..ae2e980239 100644
--- a/src/calibre/gui2/widgets2.py
+++ b/src/calibre/gui2/widgets2.py
@@ -394,7 +394,7 @@ class FlowLayout(QLayout):  # {{{
         self.do_layout(rect, apply_geometry=True)
 
     def expandingDirections(self):
-        return Qt.Orientations(0)
+        return Qt.Orientation(0)
 
     def minimumSize(self):
         size = QSize()