diff --git a/.travis.yml b/.travis.yml
index 0748f047..a870fbb8 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -19,7 +19,7 @@ jobs:
 
     - stage: test
       env: TOXENV=py35
-      python: "3.5.2"
+      python: "3.5.3"
       after_success: &after_success
         - pip install coveralls
         - coveralls
diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 6b2661e9..fc3a2b37 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -5,6 +5,7 @@ This library adheres to `Semantic Versioning 2.0 <https://semver.org/#semantic-v
 
 **UNRELEASED**
 
+- Upped the minimum Python version from 3.5.2 to 3.5.3
 - Added support for ``typing.NoReturn``
 - Added full support for ``typing_extensions`` (now equivalent to support of the ``typing`` module)
 - Added the option of supplying ``check_type()`` with globals/locals for correct resolution of
diff --git a/setup.cfg b/setup.cfg
index d95d2aa7..0560ca57 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -24,7 +24,7 @@ classifiers =
 
 [options]
 packages = typeguard
-python_requires = >= 3.5.2
+python_requires = >= 3.5.3
 zip_safe = False
 
 [options.package_data]
diff --git a/typeguard/__init__.py b/typeguard/__init__.py
index a84f6c86..d9c9a505 100644
--- a/typeguard/__init__.py
+++ b/typeguard/__init__.py
@@ -592,9 +592,6 @@ def check_type(argname: str, value, expected_type, memo: Optional[_TypeCheckMemo
     elif isclass(expected_type):
         if issubclass(expected_type, Tuple):
             check_tuple(argname, value, expected_type, memo)
-        elif issubclass(expected_type, Callable) and hasattr(expected_type, '__args__'):
-            # Needed on Python 3.5.0 to 3.5.2
-            check_callable(argname, value, expected_type, memo)
         elif issubclass(expected_type, (float, complex)):
             check_number(argname, value, expected_type)
         elif _subclass_check_unions and issubclass(expected_type, Union):