diff --git a/news/5296.bugfix.rst b/news/5296.bugfix.rst
new file mode 100644
index 0000000000..7af9507b41
--- /dev/null
+++ b/news/5296.bugfix.rst
@@ -0,0 +1 @@
+Fix an issue when using ``pipenv install --system`` on systems that having the ``python`` executable pointing to Python 2 and a Python 3 executable being ``python3``.
diff --git a/pipenv/utils/shell.py b/pipenv/utils/shell.py
index 362290fae9..f6e39bd086 100644
--- a/pipenv/utils/shell.py
+++ b/pipenv/utils/shell.py
@@ -445,7 +445,7 @@ def project_python(project, system=False):
     if not system:
         python = project._which("python")
     else:
-        interpreters = [system_which(p) for p in ("python", "python3")]
+        interpreters = [system_which(p) for p in ("python3", "python")]
         interpreters = [i for i in interpreters if i]  # filter out not found interpreters
         python = interpreters[0] if interpreters else None
     if not python:
diff --git a/tests/unit/test_utils.py b/tests/unit/test_utils.py
index 788b23eeaa..b7477b6b82 100644
--- a/tests/unit/test_utils.py
+++ b/tests/unit/test_utils.py
@@ -458,3 +458,17 @@ def test_invalid_prepare_pip_source_args(self):
         sources = [{}]
         with pytest.raises(PipenvUsageError):
             indexes.prepare_pip_source_args(sources, pip_args=None)
+
+    @pytest.mark.utils
+    def test_project_python_tries_python3_before_python_if_system_is_true(self):
+        def mock_shutil_which(command, path=None):
+            if command != "python3":
+                return f"/usr/bin/{command}"
+            return "/usr/local/bin/python3"
+
+        with mock.patch("pipenv.utils.shell.shutil.which", wraps=mock_shutil_which):
+            # Setting project to None as system=True doesn't use it
+            project = None
+            python = shell.project_python(project, system=True)
+
+        assert python == "/usr/local/bin/python3"