If in the expansion of  x3−1x2n the sum of the coefficients of x5 and x10 is 0 then the coefficient of the third term is:

Tr+1=nCrx3n−r−1x2r=nCr(−1)rx3n−5rFor coefficient of x5, set  3n−5r=5⇒r=(3n−10)/5=m(say)Note that l−m=1.We are given  nCl(−1)l+nCm(−1)m=0⇒nCl=nCm⇒l+m=n.⇒3n−55+3n−105=n⇒6n−15=5n⇒n=15.coefficient of third term =15C2(−1)2=105.