diff --git a/.appveyor.yml b/.appveyor.yml
index 2a8f44ab043f..50f752a2e47d 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -21,9 +21,6 @@ environment:
     # theoretically the CONDA_INSTALL_LOCN could be only two: one for 32bit,
     # one for 64bit because we construct envs anyway. But using one for the
     # right python version is hopefully making it fast due to package caching.
-    - PYTHON_VERSION: "3.5"
-      CONDA_INSTALL_LOCN: "C:\\Miniconda35-x64"
-      TEST_ALL: "no"
     - PYTHON_VERSION: "3.6"
       CONDA_INSTALL_LOCN: "C:\\Miniconda36-x64"
       TEST_ALL: "no"
diff --git a/.circleci/config.yml b/.circleci/config.yml
index d7c959ae0bde..2ced5f47cf57 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -97,8 +97,10 @@ jobs:
       - run: *apt-install
       - run: *fonts-install
       - run: *pip-install
-
-      - run: *deps-install
+      - run:
+           <<: *deps-install
+           environment:
+             NUMPY_VERSION: "==1.11.0"
       - run: *mpl-install
 
       - run: *doc-build
@@ -114,16 +116,9 @@ jobs:
           name: "Built documentation is available at:"
           command: echo "${CIRCLE_BUILD_URL}/artifacts/${CIRCLE_NODE_INDEX}/${CIRCLE_WORKING_DIRECTORY/#\~/$HOME}/doc/build/html/index.html"
 
-      - add_ssh_keys:
-          fingerprints:
-            - "78:13:59:08:61:a9:e5:09:af:df:3a:d8:89:c2:84:c0"
-      - deploy:
-          name: "Deploy new docs"
-          command: ./.circleci/deploy-docs.sh
-
-  docs-python35:
+  docs-python37:
     docker:
-      - image: circleci/python:3.5
+      - image: circleci/python:3.7
     steps:
       - checkout
 
@@ -131,17 +126,11 @@ jobs:
       - run: *fonts-install
       - run: *pip-install
 
-      - run:
-          <<: *deps-install
-          environment:
-            NUMPY_VERSION: "==1.11.0"
+      - run: *deps-install
       - run: *mpl-install
 
       - run: *doc-build
 
-      # We don't build the LaTeX docs here, so linkchecker will complain
-      - run: touch doc/build/html/Matplotlib.pdf
-
       - run: *doc-bundle
       - store_artifacts:
           path: doc/build/sphinx-gallery-files.tar.gz
@@ -153,6 +142,12 @@ jobs:
           name: "Built documentation is available at:"
           command: echo "${CIRCLE_BUILD_URL}/artifacts/${CIRCLE_NODE_INDEX}/${CIRCLE_WORKING_DIRECTORY/#\~/$HOME}/doc/build/html/index.html"
 
+      - add_ssh_keys:
+          fingerprints:
+            - "78:13:59:08:61:a9:e5:09:af:df:3a:d8:89:c2:84:c0"
+      - deploy:
+          name: "Deploy new docs"
+          command: ./.circleci/deploy-docs.sh
 
 #########################################
 # Defining workflows gets us parallelism.
@@ -162,5 +157,5 @@ workflows:
   version: 2
   build:
     jobs:
-      - docs-python35
       - docs-python36
+      - docs-python37
diff --git a/.travis.yml b/.travis.yml
index c3a8c2114552..40609e31d86a 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -75,13 +75,9 @@ matrix:
         - RUN_PYTEST=
         - RUN_FLAKE8=1
         - EXTRAREQS='-r requirements/testing/travis_flake8.txt'
-    - python: 3.5
-      dist: trusty
-      # pytest-cov>=2.3.1 due to https://github.com/pytest-dev/pytest-cov/issues/124.
-      env:
-        - PINNEDVERS='-c requirements/testing/travis35.txt'
     - python: 3.6
       env:
+        - PINNEDVERS='-c requirements/testing/travis36minver.txt'
         - DELETE_FONT_CACHE=1
         - EXTRAREQS='-r requirements/testing/travis36.txt'
     - python: 3.7
diff --git a/INSTALL.rst b/INSTALL.rst
index 358363bdde79..b8d940971513 100644
--- a/INSTALL.rst
+++ b/INSTALL.rst
@@ -133,7 +133,7 @@ Dependencies
 
 Matplotlib requires the following dependencies:
 
-* `Python <https://www.python.org/downloads/>`_ (>= 3.5)
+* `Python <https://www.python.org/downloads/>`_ (>= 3.6)
 * `FreeType <https://www.freetype.org/>`_ (>= 2.3)
 * `libpng <http://www.libpng.org>`_ (>= 1.2)
 * `NumPy <http://www.numpy.org>`_ (>= 1.11)
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 0f1b59707c22..b3ae38c8a57d 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -10,8 +10,6 @@ jobs:
     vmImage: 'Ubuntu 16.04'
   strategy:
     matrix:
-      Python35:
-        python.version: '3.5'
       Python36:
         python.version: '3.6'
       Python37:
diff --git a/lib/matplotlib/tests/test_animation.py b/lib/matplotlib/tests/test_animation.py
index a0cb521885fa..a99c673fa1d2 100644
--- a/lib/matplotlib/tests/test_animation.py
+++ b/lib/matplotlib/tests/test_animation.py
@@ -4,6 +4,7 @@
 import sys
 
 import numpy as np
+from pathlib import Path
 import pytest
 
 import matplotlib as mpl
@@ -123,10 +124,8 @@ def isAvailable(cls):
     ('html', 'movie.html'),
     ('null', 'movie.null')
 ]
-if sys.version_info >= (3, 6):
-    from pathlib import Path
-    WRITER_OUTPUT += [
-        (writer, Path(output)) for writer, output in WRITER_OUTPUT]
+WRITER_OUTPUT += [
+    (writer, Path(output)) for writer, output in WRITER_OUTPUT]
 
 
 # Smoke test for saving animations.  In the future, we should probably
diff --git a/requirements/testing/travis35.txt b/requirements/testing/travis35.txt
deleted file mode 100644
index 9f32b5d9c754..000000000000
--- a/requirements/testing/travis35.txt
+++ /dev/null
@@ -1,12 +0,0 @@
-# Extra pip requirements for the first travis python 3.5 build
-
-cycler==0.10
-python-dateutil==2.1
-numpy==1.11
-pandas<0.21.0
-pyparsing==2.0.1
-pytest==3.6
-pytest-cov==2.3.1
-pytest-timeout==1.2.1  # Newer pytest-timeouts don't support pytest 3.4.
-pytest-rerunfailures<5  # newer versions require pytest3.6
-sphinx==1.3
diff --git a/requirements/testing/travis36minver.txt b/requirements/testing/travis36minver.txt
new file mode 100644
index 000000000000..7e2f6208e9d3
--- /dev/null
+++ b/requirements/testing/travis36minver.txt
@@ -0,0 +1,6 @@
+# Extra pip requirements for the first travis python 3.6 build
+
+cycler==0.10
+python-dateutil==2.1
+numpy==1.11.0
+pyparsing==2.0.1