Evaluate and find the limit and, when appropriate, indicate the limit theorems (as many as you can) used. Show your complete solution.

lim┬(x→5)⁡(x^2/(x-5))

lim┬(x→-2)⁡((x^2+4x+4)/(x+2))

lim┬(〖x→0〗^- )⁡〖3/x^7 〗

lim┬(x→1)⁡〖〖2x〗^2+5x-5〗

lim┬(x→0)⁡∛(x^2-27)