diff --git a/.github/workflows/python-tests.yml b/.github/workflows/python-tests.yml
index 2ee7c0fbf5..2d5abe2767 100644
--- a/.github/workflows/python-tests.yml
+++ b/.github/workflows/python-tests.yml
@@ -24,7 +24,6 @@ jobs:
         - pypy3
         - 3.7
         - 3.6
-        - 3.5
         os:
         - ubuntu-18.04
         - ubuntu-16.04
diff --git a/.travis.yml b/.travis.yml
index 7d8c102629..8b945bd336 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -5,7 +5,6 @@ jobs:
   fast_finish: true
   include:
   - python: pypy3
-  - python: 3.5
   - python: 3.6
   - python: 3.7
   - &latest_py3
@@ -19,7 +18,7 @@ jobs:
   - arch: ppc64le
     python: pypy3
   - arch: ppc64le
-    python: 3.5
+    python: 3.6
   - &latest_py3_ppc
     arch: ppc64le
     python: 3.8
diff --git a/appveyor.yml b/appveyor.yml
index 4d1ae55f4f..8c24ec3f51 100644
--- a/appveyor.yml
+++ b/appveyor.yml
@@ -20,10 +20,6 @@ environment:
       PYTHON: "C:\\Python37-x64"
     - APPVEYOR_JOB_NAME: "python36-x64"
       PYTHON: "C:\\Python36-x64"
-    - APPVEYOR_JOB_NAME: "python35-x64"
-      PYTHON: "C:\\Python35-x64"
-      PYTEST_ADDOPTS: "--cov"
-      TOX_TESTENV_PASSENV: "PYTEST_ADDOPTS"
 
 install:
   # symlink python from a directory with a space
diff --git a/changelog.d/2435.breaking.rst b/changelog.d/2435.breaking.rst
new file mode 100644
index 0000000000..d29c60eb39
--- /dev/null
+++ b/changelog.d/2435.breaking.rst
@@ -0,0 +1 @@
+Require Python 3.6 or later.
diff --git a/setup.cfg b/setup.cfg
index 5ee3a8e98a..0d3fdcf682 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -34,7 +34,6 @@ classifiers =
     Operating System :: OS Independent
     Programming Language :: Python :: 3
     Programming Language :: Python :: 3 :: Only
-    Programming Language :: Python :: 3.5
     Programming Language :: Python :: 3.6
     Programming Language :: Python :: 3.7
     Programming Language :: Python :: 3.8
@@ -46,7 +45,7 @@ classifiers =
 
 [options]
 zip_safe = True
-python_requires = >=3.5
+python_requires = >=3.6
 py_modules = easy_install
 packages = find:
 
@@ -63,15 +62,14 @@ certs =
 tests =
     mock
     pytest-flake8
-    flake8-2020; python_version>="3.6"
+    flake8-2020
     virtualenv>=13.0.0
     pytest-virtualenv>=1.2.7
     pytest>=3.7
     wheel
     coverage>=4.5.1
-    # Coverage is unbearably slow on PyPy
-    pytest-cov>=2.5.1; python_implementation != "PyPy"
-    paver; python_version>="3.6"
+    pytest-cov>=2.5.1
+    paver
     pip>=19.1 # For proper file:// URLs support.
     jaraco.envs
     jaraco.test >= 3.1.1; python_version >= "3.6"