How do I get pictures I have taken to have a longer review time on my monitor? And I am having trouble reviewing all of the pictures I have taken on my Canon T5i.
I guess you mean that pictures show up for only few seconds on your camera's LCD after you snapped them.
First of all, you can view images for a very long time by pressing "Playback" button and scroll through images by using cross key (the one with left-right/up-down buttons).
Also, you can set how long the image is displayed on the LCD monitor immediately after capture. Consult page 204 of the manual
Finally, you should read your camera manual before asking more camera-usage related questions.