diff --git a/Tests/images/bc5_typeless.dds b/Tests/images/bc5_typeless.dds
new file mode 100644
index 000000000..b5bae52bb
Binary files /dev/null and b/Tests/images/bc5_typeless.dds differ
diff --git a/Tests/test_file_dds.py b/Tests/test_file_dds.py
index 08f200f9a..dffdf4c45 100644
--- a/Tests/test_file_dds.py
+++ b/Tests/test_file_dds.py
@@ -10,6 +10,7 @@ from .helper import assert_image_equal, assert_image_equal_tofile
 TEST_FILE_DXT1 = "Tests/images/dxt1-rgb-4bbp-noalpha_MipMaps-1.dds"
 TEST_FILE_DXT3 = "Tests/images/dxt3-argb-8bbp-explicitalpha_MipMaps-1.dds"
 TEST_FILE_DXT5 = "Tests/images/dxt5-argb-8bbp-interpolatedalpha_MipMaps-1.dds"
+TEST_FILE_DX10_BC5_TYPELESS = "Tests/images/bc5_typeless.dds"
 TEST_FILE_DX10_BC5_UNORM = "Tests/images/bc5_unorm.dds"
 TEST_FILE_DX10_BC5_SNORM = "Tests/images/bc5_snorm.dds"
 TEST_FILE_DX10_BC7 = "Tests/images/bc7-argb-8bpp_MipMaps-1.dds"
@@ -60,30 +61,23 @@ def test_sanity_dxt5():
     assert_image_equal_tofile(im, TEST_FILE_DXT5.replace(".dds", ".png"))
 
 
-def test_dx10_bc5_unorm():
-    """Check DX10 images can be opened"""
+@pytest.mark.parametrize(
+    "image_path",
+    (TEST_FILE_DX10_BC5_TYPELESS, TEST_FILE_DX10_BC5_UNORM, TEST_FILE_DX10_BC5_SNORM),
+)
+def test_dx10_bc5(image_path):
+    """Check DX10 BC5 images can be opened"""
 
-    with Image.open(TEST_FILE_DX10_BC5_UNORM) as im:
+    with Image.open(image_path) as im:
         im.load()
 
         assert im.format == "DDS"
         assert im.mode == "RGB"
         assert im.size == (256, 256)
 
-        assert_image_equal_tofile(im, TEST_FILE_DX10_BC5_UNORM.replace(".dds", ".png"))
-
-
-def test_dx10_bc5_snorm():
-    """Check DX10 images can be opened"""
-
-    with Image.open(TEST_FILE_DX10_BC5_SNORM) as im:
-        im.load()
-
-        assert im.format == "DDS"
-        assert im.mode == "RGB"
-        assert im.size == (256, 256)
-
-        assert_image_equal_tofile(im, TEST_FILE_DX10_BC5_SNORM.replace(".dds", ".png"))
+        assert_image_equal_tofile(
+            im, image_path.replace("typeless", "unorm").replace(".dds", ".png")
+        )
 
 
 def test_dx10_bc7():
diff --git a/src/PIL/DdsImagePlugin.py b/src/PIL/DdsImagePlugin.py
index dba4a5d72..21e6e0bd7 100644
--- a/src/PIL/DdsImagePlugin.py
+++ b/src/PIL/DdsImagePlugin.py
@@ -97,6 +97,7 @@ DXT5_FOURCC = 0x35545844
 DXGI_FORMAT_R8G8B8A8_TYPELESS = 27
 DXGI_FORMAT_R8G8B8A8_UNORM = 28
 DXGI_FORMAT_R8G8B8A8_UNORM_SRGB = 29
+DXGI_FORMAT_BC5_TYPELESS = 82
 DXGI_FORMAT_BC5_UNORM = 83
 DXGI_FORMAT_BC7_TYPELESS = 97
 DXGI_FORMAT_BC7_UNORM = 98
@@ -160,7 +161,7 @@ class DdsImageFile(ImageFile.ImageFile):
                 # ignoring flags which pertain to volume textures and cubemaps
                 dxt10 = BytesIO(self.fp.read(20))
                 dxgi_format, dimension = struct.unpack("<II", dxt10.read(8))
-                if dxgi_format == DXGI_FORMAT_BC5_UNORM:
+                if dxgi_format in (DXGI_FORMAT_BC5_TYPELESS, DXGI_FORMAT_BC5_UNORM):
                     self.pixel_format = "BC5"
                     n = 5
                     self.mode = "RGB"