diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index bf44d1176cc7..5cb4f5443173 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -997,6 +997,10 @@ def cla(self):
             self.xaxis.set_minor_locator(minl)
         else:
             self.xaxis._set_scale('linear')
+            try:
+                self.set_xlim(0, 1)
+            except TypeError:
+                pass
 
         if self._sharey is not None:
             self.yaxis.major = self._sharey.yaxis.major
@@ -1020,6 +1024,10 @@ def cla(self):
             self.yaxis.set_minor_locator(minl)
         else:
             self.yaxis._set_scale('linear')
+            try:
+                self.set_ylim(0, 1)
+            except TypeError:
+                pass
 
         # update the minor locator for x and y axis based on rcParams
         if (rcParams['xtick.minor.visible']):
@@ -1110,6 +1118,7 @@ def cla(self):
         if self._sharey:
             self.yaxis.set_visible(yaxis_visible)
             self.patch.set_visible(patch_visible)
+
         self.stale = True
 
     @cbook.deprecated("2.1", alternative="Axes.patch")
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 39dea8698af4..49b6a57e67ac 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -178,6 +178,54 @@ def test_twin_inherit_autoscale_setting():
     assert not ax_y_off.get_autoscaley_on()
 
 
+def test_inverted_cla():
+    # Github PR #5450. Setting autoscale should reset
+    # axes to be non-inverted.
+    # plotting an image, then 1d graph, axis is now down
+    fig = plt.figure(0)
+    ax = fig.gca()
+    # 1. test that a new axis is not inverted per default
+    assert not(ax.xaxis_inverted())
+    assert not(ax.yaxis_inverted())
+    img = np.random.random((100, 100))
+    ax.imshow(img)
+    # 2. test that a image axis is inverted
+    assert not(ax.xaxis_inverted())
+    assert ax.yaxis_inverted()
+    # 3. test that clearing and plotting a line, axes are
+    # not inverted
+    ax.cla()
+    x = np.linspace(0, 2*np.pi, 100)
+    ax.plot(x, np.cos(x))
+    assert not(ax.xaxis_inverted())
+    assert not(ax.yaxis_inverted())
+
+    # 4. autoscaling should not bring back axes to normal
+    ax.cla()
+    ax.imshow(img)
+    plt.autoscale()
+    assert not(ax.xaxis_inverted())
+    assert ax.yaxis_inverted()
+
+    # 5. two shared axes. Clearing the master axis should bring axes in shared
+    # axes back to normal
+    ax0 = plt.subplot(211)
+    ax1 = plt.subplot(212, sharey=ax0)
+    ax0.imshow(img)
+    ax1.plot(x, np.cos(x))
+    ax0.cla()
+    assert not(ax1.yaxis_inverted())
+    ax1.cla()
+    # 6. clearing the nonmaster should not touch limits
+    ax0.imshow(img)
+    ax1.plot(x, np.cos(x))
+    ax1.cla()
+    assert ax.yaxis_inverted()
+
+    # clean up
+    plt.close(fig)
+
+
 @image_comparison(baseline_images=["minorticks_on_rcParams_both"],
                   extensions=['png'])
 def test_minorticks_on_rcParams_both():
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 2b44de576dc0..f7156e07f015 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -1076,6 +1076,7 @@ def cla(self):
         # Disabling mouse interaction might have been needed a long
         # time ago, but I can't find a reason for it now - BVR (2012-03)
         #self.disable_mouse_rotation()
+        Axes.cla(self)
         self.zaxis.cla()
 
         if self._sharez is not None:
@@ -1086,11 +1087,14 @@ def cla(self):
             self.zaxis._set_scale(self._sharez.zaxis.get_scale())
         else:
             self.zaxis._set_scale('linear')
+            try:
+                self.set_zlim(0, 1)
+            except TypeError:
+                pass
 
         self._autoscaleZon = True
         self._zmargin = 0
 
-        Axes.cla(self)
 
         self.grid(rcParams['axes3d.grid'])
 
diff --git a/lib/mpl_toolkits/tests/test_mplot3d.py b/lib/mpl_toolkits/tests/test_mplot3d.py
index 7ba561c6d866..10296866e76a 100644
--- a/lib/mpl_toolkits/tests/test_mplot3d.py
+++ b/lib/mpl_toolkits/tests/test_mplot3d.py
@@ -564,3 +564,23 @@ def test_invalid_axes_limits(setter, side, value):
     obj = fig.add_subplot(111, projection='3d')
     with pytest.raises(ValueError):
         getattr(obj, setter)(**limit)
+
+
+def test_inverted_cla():
+    # Github PR #5450. Setting autoscale should reset
+    # axes to be non-inverted.
+    fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
+    # 1. test that a new axis is not inverted per default
+    assert not ax.xaxis_inverted()
+    assert not ax.yaxis_inverted()
+    assert not ax.zaxis_inverted()
+    ax.set_xlim(1, 0)
+    ax.set_ylim(1, 0)
+    ax.set_zlim(1, 0)
+    assert ax.xaxis_inverted()
+    assert ax.yaxis_inverted()
+    assert ax.zaxis_inverted()
+    ax.cla()
+    assert not ax.xaxis_inverted()
+    assert not ax.yaxis_inverted()
+    assert not ax.zaxis_inverted()