I assume you're asking to find the coefficient of the [tex]x^5y^8[/tex] term in the expansion of [tex](x+y)^{13}[/tex].
The binomial theorem says that the expansion itself is
[tex]\displaystyle(x+y)^{13}=\sum_{k=0}^{k=13}\binom{13}kx^{13-k}y^k[/tex]
and we obtain the [tex]x^5y^8[/tex] term when [tex]k=8[/tex]. So the coefficient of this term would be
[tex]\dbinom{13}8=\dfrac{13!}{8!(13-8)!}=1287[/tex]
