Determine whether the integral

${\displaystyle \underset{5}{\overset{8}{}}}\frac{t}{\sqrt[\phantom{2}]{t-5}}dt$

converges or diverges. Be sure to go through the process: guess, graph, compare, and conclude to justify your answer. To receive full credit, your solution must include:

The full process of guess, graph, compare, and conclude to justify your answer.

All the important algebraic steps along the way.