diff --git a/lib/matplotlib/backends/backend_qt5.py b/lib/matplotlib/backends/backend_qt5.py
index 7fe7ff3a476e..f70bf6f1dc5f 100644
--- a/lib/matplotlib/backends/backend_qt5.py
+++ b/lib/matplotlib/backends/backend_qt5.py
@@ -680,7 +680,6 @@ def destroy(self, *args):
         if self.window._destroying:
             return
         self.window._destroying = True
-        self.window.destroyed.connect(self._widgetclosed)
         if self.toolbar:
             self.toolbar.destroy()
         self.window.close()
diff --git a/lib/matplotlib/backends/qt_compat.py b/lib/matplotlib/backends/qt_compat.py
index 86beaf97a093..bb206c9ed3eb 100644
--- a/lib/matplotlib/backends/qt_compat.py
+++ b/lib/matplotlib/backends/qt_compat.py
@@ -102,7 +102,7 @@
 _sip_imported = False
 
 # Now perform the imports.
-if QT_API in (QT_API_PYQT, QT_API_PYQTv2, QT_API_PYQT5):
+if QT_API in (QT_API_PYQT, QT_API_PYQTv2):
     try:
         import sip
         _sip_imported = True
@@ -135,18 +135,20 @@
         except:
             res = 'QVariant API v2 specification failed. Defaulting to v1.'
             _log.info(cond + res)
-    if QT_API == QT_API_PYQT5:
-        try:
-            from PyQt5 import QtCore, QtGui, QtWidgets
-            _getSaveFileName = QtWidgets.QFileDialog.getSaveFileName
-        except ImportError:
-            if _fallback_to_qt4:
-                # fell through, tried PyQt5, failed fall back to PyQt4
-                QT_API = QT_API_PYQT
-                QT_RC_MAJOR_VERSION = 4
-            else:
-                raise
 
+if QT_API == QT_API_PYQT5:
+    try:
+        from PyQt5 import QtCore, QtGui, QtWidgets
+        _getSaveFileName = QtWidgets.QFileDialog.getSaveFileName
+    except ImportError:
+        if _fallback_to_qt4:
+            # fell through, tried PyQt5, failed fall back to PyQt4
+            QT_API = QT_API_PYQT
+            QT_RC_MAJOR_VERSION = 4
+        else:
+            raise
+
+if _sip_imported:
     # needs to be if so we can re-test the value of QT_API which may
     # have been changed in the above if block
     if QT_API in [QT_API_PYQT, QT_API_PYQTv2]:  # PyQt4 API
@@ -168,23 +170,6 @@ def _getSaveFileName(*args, **kwargs):
             # call to getapi() can fail in older versions of sip
             def _getSaveFileName(*args, **kwargs):
                 return QtGui.QFileDialog.getSaveFileName(*args, **kwargs), None
-    try:
-        # Alias PyQt-specific functions for PySide compatibility.
-        QtCore.Signal = QtCore.pyqtSignal
-        try:
-            QtCore.Slot = QtCore.pyqtSlot
-        except AttributeError:
-            # Not a perfect match but works in simple cases
-            QtCore.Slot = QtCore.pyqtSignature
-
-        QtCore.Property = QtCore.pyqtProperty
-        __version__ = QtCore.PYQT_VERSION_STR
-    except NameError:
-        # QtCore did not get imported, fall back to pyside
-        if QT_RC_MAJOR_VERSION == 5:
-            QT_API = QT_API_PYSIDE2
-        else:
-            QT_API = QT_API_PYSIDE
 
 
 if QT_API == QT_API_PYSIDE2:
@@ -211,6 +196,18 @@ def _getSaveFileName(*args, **kwargs):
     _getSaveFileName = QtGui.QFileDialog.getSaveFileName
 
 
+if QT_API in (QT_API_PYQT, QT_API_PYQTv2, QT_API_PYQT5):
+    # Alias PyQt-specific functions for PySide compatibility.
+    QtCore.Signal = QtCore.pyqtSignal
+    try:
+        QtCore.Slot = QtCore.pyqtSlot
+    except AttributeError:
+        # Not a perfect match but works in simple cases
+        QtCore.Slot = QtCore.pyqtSignature
+
+    QtCore.Property = QtCore.pyqtProperty
+    __version__ = QtCore.PYQT_VERSION_STR
+
 # Apply shim to Qt4 APIs to make them look like Qt5
 if QT_API in (QT_API_PYQT, QT_API_PYQTv2, QT_API_PYSIDE):
     '''Import all used QtGui objects into QtWidgets