About a year ago I got an EOS Rebel T5i and, it worked fine up untill a month ago. When I turn the camera to on, it says "Sensor Cleaning" and then goes to a black screen. I am still able to take pictures, but i cant change any of the settings and there is no picture preview. It works fine if I got to live view mode, but I still dont have all the options.
I hope this aren't repetitive, but did you hit "DISP"? How about have you tried "MENU"? How about Quick Control ("Q")? Do you see the aperture and shutter speed in the view finder when you press the shutter half way? If yes, great. If not then you may need Canon Tech Servicing.
What is a possibility, if you can access the MENU screen, is go to TOOLS 2 (the second wrench). Go down to LCD ON/OFF item and change it to "Shutter DISP"
If you bought this camera used, here is a copy of the manual. http://gdlp01.c-wss.com/gds/2/0300014592/02/eos-rebelt5-1200d-im3-en.pdf
Good luck. The T5 is a nice camera. Just remember, it isn't environmentally sealed so keep it away from moisture.
The display screen can cycle through several things that it can optionally display, but one of the choices is simply to remain black. I use this when I do astrophotography to protect my night vision.
If it's working when you use Liveview, shows the sensor cleaning, and can display the menu, then there's probably nothing wrong with the camera and likely you've just got the display in the mode where it remains dark.
Just left of the eyecup is a button labeled "Info." Just press that button a few times. Each time you press it, it switches to the next optional display mode. (there are only a few of them) and then back to the beginning of it's list -- it loops through the choices.)
Tap the "Info." button until you get the display that you want.
BTW, this also works when reviewing images. Normally you see the image (full screen) but it has choices to show you the image, with or without shooting info & filename, it has a display where it shows the histogram, etc.
On some camera models this button was labeled "Disp." instead of "Info." but I think on your model it will say "Info."