diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index aa10369..eababa6 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -21,12 +21,6 @@ jobs:
         # The forced pytest versions correspond with the lower bounds in tox.ini
         pytest-version: ['', '--force-dep pytest==4', '--force-dep pytest==6.2.4']
         include:
-        - os: 'ubuntu-20.04'
-          python-version: '3.5'
-          pytest-version: ''
-        - os: 'ubuntu-20.04'
-          python-version: '3.5'
-          pytest-version: '--force-dep pytest==4'
         - os: 'ubuntu-20.04'
           python-version: '3.6'
         exclude:
diff --git a/pyproject.toml b/pyproject.toml
index 6eb8170..6c4b23b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -6,5 +6,5 @@ build-backend = "setuptools.build_meta"
 write_to = "pytest_localserver/_version.py"
 
 [tool.black]
-target-version = ['py35']
+target-version = ['py36']
 line-length = 120
diff --git a/pytest_localserver/smtp.py b/pytest_localserver/smtp.py
index 532d80a..0b285eb 100644
--- a/pytest_localserver/smtp.py
+++ b/pytest_localserver/smtp.py
@@ -95,16 +95,7 @@ def is_alive(self):
 
     @property
     def accepting(self):
-        try:
-            return self.server.is_serving()
-        except AttributeError:
-            # asyncio.base_events.Server.is_serving() only exists in Python 3.6
-            # and up. For Python 3.5, asyncio.base_events.BaseEventLoop.is_running()
-            # is a close approximation; it should mostly return the same value
-            # except for brief periods when the server is starting up or shutting
-            # down. Once we drop support for Python 3.5, this branch becomes
-            # unnecessary.
-            return self.loop.is_running()
+        return self.server.is_serving()
 
     # for aiosmtpd <1.4
     if not hasattr(aiosmtpd.controller.Controller, "_trigger_server"):
diff --git a/setup.py b/setup.py
index 438c4a3..d3b0d31 100644
--- a/setup.py
+++ b/setup.py
@@ -38,7 +38,7 @@ def run(self):
     long_description=read("README.rst"),
     url="https://github.com/pytest-dev/pytest-localserver",
     packages=["pytest_localserver"],
-    python_requires=">=3.5",
+    python_requires=">=3.6",
     install_requires=["werkzeug>=0.10"],
     extras_require={
         "smtp": [
@@ -59,7 +59,6 @@ def run(self):
         "License :: OSI Approved :: MIT License",
         "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",
diff --git a/tox.ini b/tox.ini
index 263b570..cf9b349 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py{35,36,37,38,39,310,311,312,py3}{,-smtp},lint
+envlist = py{36,37,38,39,310,311,312,py3}{,-smtp},lint
 recreate = True
 isolated_build = True