diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 1750a764a..a85e3c8fb 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -8,8 +8,11 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        name: [py36, py37]
+        name: [py35, py36, py37]
         include:
+        - name: py35
+          python: 3.5
+          docutils: du12
         - name: py36
           python: 3.6
           docutils: du13
diff --git a/.travis.yml b/.travis.yml
index 8e971a356..4123ba6b5 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -11,9 +11,6 @@ env:
 
 jobs:
   include:
-    - python: '3.5'
-      env:
-        - TOXENV=du12
     - python: '3.8'
       env:
         - TOXENV=du15
diff --git a/tests/test_ext_autodoc.py b/tests/test_ext_autodoc.py
index c0676f23f..703cc13f6 100644
--- a/tests/test_ext_autodoc.py
+++ b/tests/test_ext_autodoc.py
@@ -1832,19 +1832,26 @@ def test_autodoc_for_egged_code(app):
 def test_singledispatch(app):
     options = {"members": None}
     actual = do_autodoc(app, 'module', 'target.singledispatch', options)
-    assert list(actual) == [
-        '',
-        '.. py:module:: target.singledispatch',
-        '',
-        '',
-        '.. py:function:: func(arg, kwarg=None)',
-        '                 func(arg: int, kwarg=None)',
-        '                 func(arg: str, kwarg=None)',
-        '   :module: target.singledispatch',
-        '',
-        '   A function for general use.',
-        '',
-    ]
+    if sys.version_info < (3, 6):
+        # check the result via "in" because the order of singledispatch signatures is
+        # usually changed (because dict is not OrderedDict yet!)
+        assert '.. py:function:: func(arg, kwarg=None)' in actual
+        assert '                 func(arg: int, kwarg=None)' in actual
+        assert '                 func(arg: str, kwarg=None)' in actual
+    else:
+        assert list(actual) == [
+            '',
+            '.. py:module:: target.singledispatch',
+            '',
+            '',
+            '.. py:function:: func(arg, kwarg=None)',
+            '                 func(arg: int, kwarg=None)',
+            '                 func(arg: str, kwarg=None)',
+            '   :module: target.singledispatch',
+            '',
+            '   A function for general use.',
+            '',
+        ]
 
 
 @pytest.mark.skipif(sys.version_info < (3, 8),
diff --git a/tests/test_ext_autodoc_autofunction.py b/tests/test_ext_autodoc_autofunction.py
index bb292bc6a..1f68c0319 100644
--- a/tests/test_ext_autodoc_autofunction.py
+++ b/tests/test_ext_autodoc_autofunction.py
@@ -9,6 +9,8 @@
     :license: BSD, see LICENSE for details.
 """
 
+import sys
+
 import pytest
 
 from test_ext_autodoc import do_autodoc
@@ -108,16 +110,23 @@ def test_decorated(app):
 def test_singledispatch(app):
     options = {}
     actual = do_autodoc(app, 'function', 'target.singledispatch.func', options)
-    assert list(actual) == [
-        '',
-        '.. py:function:: func(arg, kwarg=None)',
-        '                 func(arg: int, kwarg=None)',
-        '                 func(arg: str, kwarg=None)',
-        '   :module: target.singledispatch',
-        '',
-        '   A function for general use.',
-        '',
-    ]
+    if sys.version_info < (3, 6):
+        # check the result via "in" because the order of singledispatch signatures is
+        # usually changed (because dict is not OrderedDict yet!)
+        assert '.. py:function:: func(arg, kwarg=None)' in actual
+        assert '                 func(arg: int, kwarg=None)' in actual
+        assert '                 func(arg: str, kwarg=None)' in actual
+    else:
+        assert list(actual) == [
+            '',
+            '.. py:function:: func(arg, kwarg=None)',
+            '                 func(arg: int, kwarg=None)',
+            '                 func(arg: str, kwarg=None)',
+            '   :module: target.singledispatch',
+            '',
+            '   A function for general use.',
+            '',
+        ]
 
 
 @pytest.mark.sphinx('html', testroot='ext-autodoc')