Five consecutive cards can be chosen out of $13$ cards in $9$ ways. $\left(\mathrm{2,3},\mathrm{4,5},6\right),\left(\mathrm{3,4},\mathrm{5,6},7\right),......\left(10,J,Q,K,A\right).$ The first card can be chosen in $4$ ways (spades, hearts, diamonds and clubs). The second and the subsequent cards, too, can be chosen in $4$ ways.
Thus, there are $4^5$ ways to choose the five cards.
The number of ways in which all the five cards are not from the same suit is $4^5-4=1020.$
So, the number of straights in this case is $m=9\times 1020\Rightarrow \frac{m}{1500}=\frac{9\times 102\cancel{0}}{150\cancel{0}}=6.12$