5: You should get
This is essentially a ratio of polynomials, so the appropriate tricks should work (see the box "polynomials and ratios with powers"). Determine dominant powers and factor.
Since you got rid of the indeterminate difference, it should now be possible to determine the type of this limit: It is infinity over infinity. Could you use the l'Hospital rule? Yes, but the root suggests that it is not exactly the best idea. Try it, it is a bit more work but using it twice should lead to the answer.