diff --git a/.travis.yml b/.travis.yml
index ebbfd9d8..795ea320 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,7 +1,6 @@
 dist: xenial  # required for Python >= 3.7
 language: python
 python:
-  - "3.5"
   - "3.6"
   - "3.7"
   - "3.8"
@@ -11,7 +10,7 @@ matrix:
     - python: "nightly"
 install:
   - "pip install --editable .[with_everything]"
-  - "pip install safety pipenv numpy tzlocal nose coverage coveralls -U"
+  - "pip install safety pipenv numpy tzlocal nose coverage coveralls py -U"
   - "pip freeze | safety check --stdin"
 script:
   - "nosetests -s --with-coverage --cover-inclusive --cover-package=prospector tests/"
diff --git a/CONTRIBUTING.rst b/CONTRIBUTING.rst
index cc89615e..dae1a4b3 100644
--- a/CONTRIBUTING.rst
+++ b/CONTRIBUTING.rst
@@ -37,7 +37,7 @@ handling the output of other tools. However, please do run them before submittin
 
     nosetests tests/
 
-Prospector targets Python 2.7, 3.4, 3.5, 3.6, 3.7 and 3.8. You can use `tox`_ to test this locally,
+Prospector targets Python 2.7, 3.6, 3.7 and 3.8. You can use `tox`_ to test this locally,
 and all tests are run on `travis-ci.org`_.
 
 .. _tox: https://tox.readthedocs.io/en/latest/
diff --git a/docs/contrib.rst b/docs/contrib.rst
index 4551c71d..abe9b908 100644
--- a/docs/contrib.rst
+++ b/docs/contrib.rst
@@ -37,7 +37,7 @@ handling the output of other tools. However, please do run them before submittin
 
     nosetests tests/
 
-Prospector targets Python 3.5, 3.6, 3.7 and 3.8. You can use `tox`_ to test this locally,
+Prospector targets Python 3.6, 3.7, and 3.8. You can use `tox`_ to test this locally,
 and all tests are run on `travis-ci.org`_.
 
 .. _tox: https://tox.readthedocs.io/en/latest/
diff --git a/prospector/tools/pylint/__init__.py b/prospector/tools/pylint/__init__.py
index d9dcc2fa..9ce0c7d7 100644
--- a/prospector/tools/pylint/__init__.py
+++ b/prospector/tools/pylint/__init__.py
@@ -79,7 +79,7 @@ def _prospector_configure(self, prospector_config, linter):
         # allow the indentation specified in the pylint configuration file; we
         # replace it instead with our own version which is more lenient and
         # configurable
-        linter.disable("mixed-indentation")
+        linter.disable("mixed-indentation", ignore_unknown=True)
         indent_checker = IndentChecker(linter)
         linter.register_checker(indent_checker)
 
diff --git a/setup.py b/setup.py
index 416f7699..ef11a7e8 100644
--- a/setup.py
+++ b/setup.py
@@ -11,8 +11,8 @@
     exec(f.read())
 _VERSION = globals()["__version__"]
 
-if sys.version_info < (3, 5):
-    raise Exception("Prospector %s requires Python 3.5 or higher." % _VERSION)
+if sys.version_info < (3, 6):
+    raise Exception("Prospector %s requires Python 3.6 or higher." % _VERSION)
 
 
 _PACKAGES = find_packages(exclude=["*.tests", "*.tests.*", "tests.*", "tests"])
@@ -30,9 +30,9 @@
     "pycodestyle<2.7.0,>=2.6.0",
     "pep8-naming>=0.3.3,<=0.10.0",
     "pydocstyle>=2.0.0",
-    "pylint==2.5.3",
+    "pylint==2.7.2",
     "pylint-django<2.2.0",
-    "astroid==2.4.1",
+    "astroid==2.5.1",
 ]
 
 
@@ -46,7 +46,6 @@
     "Intended Audience :: Developers",
     "Operating System :: Unix",
     "Topic :: Software Development :: Quality Assurance",
-    "Programming Language :: Python :: 3.5",
     "Programming Language :: Python :: 3.6",
     "Programming Language :: Python :: 3.7",
     "Programming Language :: Python :: 3.8",
diff --git a/tox.ini b/tox.ini
index d3aeb967..c57a762f 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py35,py36,py37,py38
+envlist = py36,py37,py38
 
 skip_missing_interpreters = true