Rank and please provide a detailed explanation, don't just provide the final series.

Rank the following functions in asymptotically increasing order based on O-notation and justify your ordering (using the limit test): 5n, 4 log n, 4 log log n, n^4, n^1/2 log^4 n, n^log n, 5^n, 4^n^4, 5^5n, 4^4^n, n^n/4, n^n^1/5