In event space for a standard pack of 52 playing cards. Assume there are no wild cards. Consider 5-card hands.
Compute the conditional probability of a straight flush given that the first two cards you are dealt are the 9 and 10 of hearts.
my guess is 4/(52 C 5) but I am really unsure
You are almost right. There are four possibilities for a straight flush. But the total number of possible hands is not $52\choose 5$, because two cards have already been dealt; it is $50\choose 3$.
So the answer is $\dfrac{4}{50\choose 3}$.