Why would amplitude modulation result in change of frequency?
$$A[1+\mu\cos(2\pi 5000t)]\sin(2\pi 2000000t)= A\sin(2\pi 2000000t) + \dfrac{A\mu}{2}(\sin(2\pi[2000000-5000]t)+\sin(2\pi[2000000+5000]t))$$

If I didn't make an error with my trigonometric identities.

The three distinct frequencies are there: the carrier and the positive and negative frequency version of the tone around the carrier.

The above assumes an AM that is not suppressed carrier, since the problem statement didn't say "suppressed carrier".