He has 5 pennies and 5 nickels in his pocket.
If he pick two coins in a row, we have to compare the probabilities of getting two pennies or one penny and one nickel. We will assume that there is no reposition: the coin that is drawn is not put again in the pocket.
Probability of getting two pennies:
For the first draw, it has p=0.5 (50% of chances) of getting a penny, as there are 10 coins and 5 of them are pennies.
Then, for the second draw there is p=4/9=0.44 chances of getting a penny, as one has already been picked.
Then, the probability of getting two pennies in a row is:

Probability of getting one penny and one nickel:
For the first draw, we can get pennies or nickels. Both of them are valid, so we will have a probability of p=1 for the first draw.
Then, for the second draw, we have to pick the other category: if we had a penny in the first draw, we should get a nickel in the second one and, if we had a nickel in the first draw, we should get a penny in the second draw.
In both cases, there will be 5 coins of the other category out of the 9 remaining coins.
Then, the probability of success in the second draw is p=5/9=0.55.
Then, the probability of getting one nickel and one penny is:

Answer: it is more likely that he will pick out one penny and a nickel.