The radius of the moon's orbit is increasing by 3.8 cm/year as has been measured with great accuracy using the laser reflectors installed on the moon by Apollo 11. If you used energy considerations, the calculation would say that the moon would spiral into the earth. However, tidal forces are important and, since the tidal motions of the earth and moon are not conservative (due to friction as the water and solid material move due to the tidal forces), you cannot use those simple energy considerations. However, angular momentum is conserved. Since the bulge in the earth due to the moon's tidal force is a little ahead of lining up exactly with the moon's position due to the earth's rotation, it increases the angular momentum of the moon in its orbit around the earth. This takes angular momentum from the earth's rotation and transfers it to the moon's orbit. This will continue for about 2 billion years at which time the earth and moon will always face each other with the same side. Since the angular momentum is given by L = mvR, and v is decreased, R is increased, explaining the increase in the radius of the orbit.
