Answer
Coefficient of $x^{5}$$y^{8}$ is 1287.
Work Step by Step
We know by Binomial theorem
$(x+y)^{n}$ = C(n,0)$x^{n}$ + C(n,1)$x^{n-1}$$y^{1}$ .... + C(n,n)$y^{n}$
Coefficient of $x^{n-j}$$y^{j}$ = C(n,j)
In our case n = 13 , j = 5
So coefficient = C(13,5) = 1287