Question: difficult numerical integration

Why is this integral so difficult -- so slow to execute?

seq(evalf(Int(1/R*sinh(s*coth(1/2*s))^(2*I/k)/(gam-I*k*cosh(s))^5*
     Int(exp(-(k^2*sinh(s)^2/(gam-I*k*cosh(s))-I*k*(1+cosh(s)))*v)*
     hypergeom([1/k*I],[1],k*v*I)*v^n,v = 0 .. 1/2*R), s=0..s_max)), n=0..1);

Hints to improve the efficiency of execution would be appreciated.

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