Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and the Binomial Theorem - 10.2 Exercises - Skill Practice - Page 694: 16

$2574$

We know that if we want to select $r$ objects out of $n$ disregarding the order, we can do this in $_nC_r=\frac{n!}{r!(n-r)!}$ ways. Here we have $n=13$ and $r=5$, but we must multiply this by $2$ because it can be hearts or diamonds. Hence the answer: $2\cdot(_{13}C_5)=\frac{13!}{8!5!}=2\cdot1287=2574$