It is easier to learn to shoot video with a fully manual lens. But, it helps to be good still photographer before you start shooting video. Many videographers will take a few stills of the scene before they record video, if at all possible. It helps them get an idea of what exposure settings to use. And, it also helps in setting White Balance, and getting color reproduction correct.
As for your immediate problem, try taking photos in Manual shooting mode with ISO set to Auto.
The T5 is not well suited for video. One by one, you are encountering all of the reasons why one would want to use a fully manual lens when shooting video. Take a look at Rokinon Cinema lenses. My first was the 14mm T3.1, and I love it.
In a way, you do not really want to adjust ISO on the fly, as you record video. Changing the ISO can result in sudden jumps in the apparent brightness of an image. The same is true when adjusting aperture while recording video. For this reason, cinema lenses have a “declicked” aperture ring, so that you can continuously adjust it, instead of changing in discrete steps.
As far as adjusting exposure with the T5, this seems to be done by the camera. You have no control over it, AFAIK.
According to the T5 user's manual...
on page 156...
...You should be able to adjust manual exposure settings for shooting video. I'd start out with maybe 1/60 sec. shutter speed and adjust aperture and ISO to suit your lighting conditions. The exposure settings should be the same as you'd use for still shooting under the same lighting conditions.
Your present lens should work well enough to get you started and for some experimentation.