There are 5+5 = 10 coins total, of which 5 are dimes. The probability of selecting a dime is 5/10 = 1/2.
The coin is not put back, so we have 10-1 = 9 coins overall. Of this, 5 are pennies. The probability of pulling a penny out is 5/9. Note how this is dependent on the first event above.
From here, multiply the two probabilities
(1/2)*(5/9) = 5/18
The rule used here is
P(A and B) = P(A)*P(B given A)
where A and B are the events "pulling out a dime on the first selection" and "pulling out a penny on the second selection"
