let u = x^4 - 4 and du = 4x^3 dx

x^5 can be split up into (x^3)(x^2) so when you make the substitutions, you integral will become: (1/4) integral of x^2 / sqrt(u) du. now to get x^2 in terms of u, take our original substitution u = x^4 - 4 and solve for x^2.

x^4 = u + 4 so x^2 = sqrt(u+4) so the integral will become: (1/4)integral of sqrt[(u+4)/(u)] du. the integrand can be further simplified to sqrt(1 + 4/x) = sqrt(1 + (2/sqrt(x))^2). now consult your integral table and find the form that matches this and finish up.