Is it possible to adjust the Canon Rebel T5's exposure length beyond 30 seconds, and if so how? Thanks in advance.
You want to use Bulb mode. With the EOS Rebel T5/1200D you can access Bulb mode by selecting Manual exposure mode and turning the control dial all the way to the left.
In Bulb mode the shutter opens when you press the shutter button and stays open until the shutter button is released. In order to avoid camera movement when using bulb mode many people use a wired remote shutter release. Many of them allow the shutter button to be locked down so the shutter stays open without having to continually press the button. Others even have a built in timer that can be set to take a series of pictures with a specific shutter time and at a specific interval.
Take as many successive images at 30 seconds (or less) as needed to reach the wanted exposure time, and sum the images in post-processing.