Thats a pretty good game since you didn't mention any fee for playing it...
Hint Your profit is 4X, where X~Bi(5, [13/52])
Can you calculate the Mean, variance of X?
And hence can you find the Mean, Variance of 4X?
If you haven't been taught how to do the above, then you can alternatively calculate the probability distribution of profit:
tips on how to do that are in the spoiler, but using the hint above is faster and easier.