How do you read powers and roots?
Your propositions are all correct. "4th root of five" can be read as "quad root of five", but 4-th root is no way incorrect and both ways are interchangeable. Similarly "fifth root" and "quintic root" are both acceptable. When you get to say 6th root people would understand it easier if you read "sixth root" than "hex root". This ought to answer your question on x√2 as well, with generalised reading of "x-th root of two".
5^3 is read "five cubed". For a^x you simply read "a to the power of x" for x greater than or equal to 4.