First, let’s pick the two ranks to have the two pair in. There are 13 ranks, so this is 13C2 = 78.

Next, the number of ways to pick each pair from the 4 cards of each rank is 4C2 = 6.

There are 44 cards left which are not of either rank of the pairs. So the total number of hands with two pair is 78 * 6 * 6 * 44 = 123552.

Finally, the total number of 5-card hands is 52C5 = 2598960. Thus the probability of two pair is 123552/2598960 = 198/4165. That’s about 4.75%.