The straights are these 10 
A,2,3,4,5
2,3,4,5,6
3,4,5,6,7
4,5,6,7,8
5,6,7,8,9
6,7,8,9,10
7,8,9,10,J
8,9,10,J,Q
9,10,J,Q,K
10,J,Q,K,A

and for each of those 10 ways, the 5 cards

can have any of 4 suits each, so the

total number of hands in sequence is 10×4×4×4×4×4 = 10×45 = 10240

However this 10240 contain the straight flushes in which all
five cards have the same suit, so we must subtract the straight
flushes.  To find the number of straight flushes, we can choose
the sequence any of 10 ways and the common suit any of 4 ways,
so that's  10×4 or 40 straight flushes we must subtract from the
10240, so the answer is 10240-40 or 10200.

Edwin