diff --git a/README.md b/README.md
index 4a6ba577..6de03844 100644
--- a/README.md
+++ b/README.md
@@ -302,6 +302,7 @@ for family, grp in itertools.groupby(collected.checks.items(), key=lambda x: x[1
 - [`PP002`](https://learn.scientific-python.org/development/guides/packaging-simple#PP002): Has a proper build-system table
 - [`PP003`](https://learn.scientific-python.org/development/guides/packaging-classic#PP003): Does not list wheel as a build-dep
 - [`PP004`](https://learn.scientific-python.org/development/guides/packaging-simple#PP004): Does not upper cap Python requires
+- [`PP005`](https://learn.scientific-python.org/development/guides/packaging-simple#PP005): Using SPDX project.license should not use deprecated trove classifiers
 - [`PP301`](https://learn.scientific-python.org/development/guides/pytest#PP301): Has pytest in pyproject
 - [`PP302`](https://learn.scientific-python.org/development/guides/pytest#PP302): Sets a minimum pytest to at least 6
 - [`PP303`](https://learn.scientific-python.org/development/guides/pytest#PP303): Sets the test paths
diff --git a/docs/_includes/pyproject.md b/docs/_includes/pyproject.md
index bf8e6b5f..41fedee2 100644
--- a/docs/_includes/pyproject.md
+++ b/docs/_includes/pyproject.md
@@ -45,6 +45,22 @@ You can read more about each field, and all allowed fields, in
 or [Whey](https://whey.readthedocs.io/en/latest/configuration.html). Note that
 "Homepage" is special, and replaces the old url setting.
 
+### License
+
+The license can be done one of two ways. The classic convention (shown above)
+uses one or more [Trove Classifiers][] to specify the license. The other way is
+to use the `license` field and an [SPDX identifier expression][spdx]:
+
+```toml
+license = "BSD-3-Clause"
+```
+
+You can also specify files to include with the `license-files` field.
+
+You should not include the `License ::` classifiers if you use the `license`
+field {% rr PP007 %}. Some backends do not support this fully yet (notably
+Poetry and Setuptools).
+
 ### Extras
 
 It is recommended to use extras instead of or in addition to making requirement
@@ -85,3 +101,5 @@ function, followed by a colon, then the function to call. If you use
 work to call the app (`__name__` will be `"__main__"` in that case).
 
 [metadata]: https://packaging.python.org/en/latest/specifications/core-metadata/
+[trove classifiers]: https://pypi.org/classifiers/
+[spdx]: https://spdx.org/licenses
diff --git a/pyproject.toml b/pyproject.toml
index 2add3fb1..8fa544ad 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -10,13 +10,13 @@ authors = [
 ]
 description = "Review repos for compliance to the Scientific-Python development guidelines"
 requires-python = ">=3.10"
+license-expression = 'BSD-3-Clause'
 classifiers = [
   "Development Status :: 4 - Beta",
   "Environment :: Console",
   "Environment :: WebAssembly :: Emscripten",
   "Intended Audience :: Developers",
   "Intended Audience :: Science/Research",
-  "License :: OSI Approved :: BSD License",
   "Operating System :: OS Independent",
   "Programming Language :: Python :: 3",
   "Programming Language :: Python :: 3.10",
diff --git a/src/sp_repo_review/checks/pyproject.py b/src/sp_repo_review/checks/pyproject.py
index ef0bbc41..8f6be23b 100644
--- a/src/sp_repo_review/checks/pyproject.py
+++ b/src/sp_repo_review/checks/pyproject.py
@@ -94,6 +94,29 @@ def check(pyproject: dict[str, Any], package: Traversable) -> bool | None:
         return None
 
 
+class PP005(PyProject):
+    "Using SPDX project.license should not use deprecated trove classifiers"
+
+    requires = {"PY001"}
+    url = mk_url("packaging-simple")
+
+    @staticmethod
+    def check(pyproject: dict[str, Any]) -> bool | None:
+        """
+        If you use SPDX identifiers in `project.license`, then all the `License ::`
+        classifiers are deprecated.
+
+        See https://packaging.python.org/en/latest/specifications/core-metadata/#license-expression
+        """
+        match pyproject:
+            case {"project": {"license": str(), "classifiers": classifiers}}:
+                return all(not c.startswith("License ::") for c in classifiers)
+            case {"project": {"license": str()}}:
+                return True
+            case _:
+                return None
+
+
 class PP301(PyProject):
     "Has pytest in pyproject"
 
diff --git a/tests/packages/ruff_extend/ruff.toml b/tests/packages/ruff_extend/ruff.toml
index b8c006e9..00c86cbb 100644
--- a/tests/packages/ruff_extend/ruff.toml
+++ b/tests/packages/ruff_extend/ruff.toml
@@ -1,2 +1,2 @@
 extend = "pyproject.toml"
-target-version = "3.9"
+target-version = "py39"
diff --git a/tests/test_pyproject.py b/tests/test_pyproject.py
index ff283b8a..abf65037 100644
--- a/tests/test_pyproject.py
+++ b/tests/test_pyproject.py
@@ -113,6 +113,55 @@ def test_PP004_not_present(tmp_path: Path):
     assert compute_check("PP004", pyproject={}, package=tmp_path).result is None
 
 
+def test_PP005_no_license():
+    toml = toml_loads("""
+        [project]
+        license.text = "MIT"
+        classifiers = ["License :: OSI Approved :: MIT License"]
+        """)
+
+    assert compute_check("PP005", pyproject=toml).result is None
+
+
+def test_PP005_pass():
+    toml = toml_loads("""
+        [project]
+        license = "MIT"
+        """)
+
+    assert compute_check("PP005", pyproject=toml).result
+
+
+def test_PP005_pass_empty_classifiers():
+    toml = toml_loads("""
+        [project]
+        license = "MIT"
+        classifiers = []
+        """)
+
+    assert compute_check("PP005", pyproject=toml).result
+
+
+def test_PP005_pass_other_classifiers():
+    toml = toml_loads("""
+        [project]
+        license = "MIT"
+        classifiers = ["Something :: Else"]
+        """)
+
+    assert compute_check("PP005", pyproject=toml).result
+
+
+def test_PP005_both():
+    toml = toml_loads("""
+        [project]
+        license = "MIT"
+        classifiers = ["License :: OSI Approved :: MIT License"]
+        """)
+
+    assert not compute_check("PP005", pyproject=toml).result
+
+
 def test_PP302_okay_intstr():
     toml = toml_loads("""
         [tool.pytest.ini_options]