Combinations/permutations problem

How many ways are there to draw a 4, 5, 6, 7 and 8 from a deck of 52 standard cards, with the condition that not all the cards are the same suit?

I think this is combinations problem, with 5 separate 4C1 equations that I multiply together. But how do I account for the suits not all being the same?

total # of combos = (4c1)^5 = 4^5 = 1024
minus # of combos with all from same suit = 4c1 = 4
ans: 1020
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