There are a couple mistakes:
- It seems like you are computing the probability of drawing those cards in that order, when instead you want to compute the probability of having a hand containing these cards in some order.
- You have not ensured that the fifth card is not an ace or a king.
There are various ways to get the right answer; here is one of them.
There are $\binom{52}{5} = 52 \cdot 51 \cdot 50 \cdot 49 \cdot 48 / 5!$ possible hands of five cards, without accounting for order. This will be your denominator.
For the numerator we need to count how many valid hands are possible.
There are $3$ choices for the non-heart ace.
There are $\binom{4}{2}=6$ choices for the pair of kings.
There are $44$ cards that are not kings or aces.
So the numerator is $3 \cdot 6 \cdot 44$.
Another way is to count the number of valid ordered hands and divide by the total number of ordered hands $52 \cdot 51 \cdot 50 \cdot 49 \cdot 48$. What you will end up with is $5!$ times the numerator computed by the above method, so the final answer is the same.