diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 5ef8405..fef66e2 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -11,7 +11,7 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: [3.5, 3.6, 3.7, 3.8, 3.9]
+        python-version: [3.7, 3.8, 3.9]
 
     steps:
     - uses: actions/checkout@v2
diff --git a/NEWS.md b/NEWS.md
index a142bfa..1cf5f78 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,9 @@
 User-visible changes in "magic-wormhole":
 
+## Upcoming Release
+
+* Python 3.5 and 3.6 are past their EOL date and support is dropped (#448)
+
 ## Release 0.12.0 (04-Apr-2020)
 
 * A command like `wormhole send /dev/fd0` can send the contents of the named
diff --git a/tox.ini b/tox.ini
index 914b22e..e1e6e8b 100644
--- a/tox.ini
+++ b/tox.ini
@@ -4,8 +4,8 @@
 # and then run "tox" from this directory.
 
 [tox]
-# useful envs: py27-nodilate, py35, py36, py37, py38, pypy, flake8
-envlist = {py27-nodilate,py35,py36,py37,py38}
+# useful envs: py27-nodilate, py37, py38, pypy, flake8
+envlist = {py27-nodilate,py37,py38}
 skip_missing_interpreters = True
 minversion = 2.4.0