diff --git a/PyInstaller/hooks/hook-PyQt5.py b/PyInstaller/hooks/hook-PyQt5.py
index 6742f68b4bc..52254613a85 100644
--- a/PyInstaller/hooks/hook-PyQt5.py
+++ b/PyInstaller/hooks/hook-PyQt5.py
@@ -6,6 +6,7 @@
 #
 # The full license is in the file COPYING.txt, distributed with this software.
 #-----------------------------------------------------------------------------
+import glob
 import os
 
 from PyInstaller.utils.hooks import pyqt5_library_info, collect_system_data_files
@@ -18,16 +19,34 @@
                                    'PyQt5')
          if os.path.basename(x[0]) == 'qt.conf']
 
-# Include ICU files, if they exist. See the "Deployment approach" section in
-# ``PyInstaller/utils/hooks/qt.py``.
-[(os.path.join(pyqt5_library_info.location['BinariesPath'], dll),
-  os.path.join('PyQt5', 'Qt', 'bin', dll))
- for dll in ('icudt??.dll', 'icuin??.dll', 'icuuc??.dll')]
+dlls_to_include = [
+    # TODO: Uncomment when the standard PyQt5 wheel includes d3dcompiler_XX.dll
+    # 'libEGL.dll', 'libGLESv2.dll', 'd3dcompiler_??.dll',  # ANGLE fallback
+    'opengl32sw.dll',  # OpenGL software renderer fallback
+    'icudt??.dll', 'icuin??.dll', 'icuuc??.dll'  # ICU files
+    # See  "Deployment approach" section in ``PyInstaller/utils/hooks/qt.py``
+]
+binaries = []
+for dll in dlls_to_include:
+    dll_path = os.path.join(pyqt5_library_info.location['BinariesPath'], dll)
+    dll_file_paths = glob.glob(dll_path)
+    # Only add files if they exist.
+    for dll_file_path in dll_file_paths:
+        file_name = os.path.basename(dll_file_path)
+        dst_dll_path = os.path.join('PyQt5', 'Qt', 'bin', file_name)
+        binaries.append((dll_file_path, dst_dll_path))
 
-# TODO: Include software rendering for OpenGL. See the "Deployment approach". However, because the standard PyQt5 wheel `doesn't include <https://www.riverbankcomputing.com/pipermail/pyqt/2018-June/040387.html>`_ ``d3dcompiler_XX.dll``, this produces failures. When the wheel is updated, this code can be uncommented.
-##binaries = []
-##for dll in ('libEGL.dll', 'libGLESv2.dll', 'd3dcompiler_??.dll', 'opengl32sw.dll'):
-##    dll_path = os.path.join(pyqt5_library_info.location['BinariesPath'], dll)
-##    # Only add files if they exist.
-##    if glob(dll_path):
-##        binaries += [(dll_path, os.path.join('PyQt5', 'Qt', 'bin', dll))]
+# TODO: Once the PyQt5 wheels include d3dcompiler_??.dll remove this
+# Only include ANGLE if all files are available, this prevents CI failure
+angle_binaries = []
+for dll in ('libEGL.dll', 'libGLESv2.dll', 'd3dcompiler_??.dll'):
+    dll_path = os.path.join(pyqt5_library_info.location['BinariesPath'], dll)
+    dll_file_paths = glob.glob(dll_path)
+    # Only add files if they exist.
+    for dll_file_path in dll_file_paths:
+        file_name = os.path.basename(dll_file_path)
+        dst_dll_path = os.path.join('PyQt5', 'Qt', 'bin', file_name)
+        angle_binaries.append((dll_file_path, dst_dll_path))
+
+if len(angle_binaries) == 3:
+    binaries += angle_binaries