The moon is being continually boosted by the rotation of the earth. The moon's gravity causes tides on the earth's surface. However, the shape of the earth is slightly ahead of being directly lined up with the moon because of inertia and sloshing. That uneven earth shape exerts a slightly uneven pull on the moon which increases its angular velocity around the earth, and slows down the angular velocity of the earth's rotation.

     .--~~~--.             ^
    /   <-    \            |
   |   Earth  |            O Moon
   \    ->   /
    '--___--'

Note, the bulge of the earth is slightly exaggerated in this diagram, and the moon is further away on this scale.

In effect, the rotation of the earth is dragging the moon around faster (which causes it to move further from the earth and go slower).

The moon is actually moving away from the earth.