Greetings Cesar1996,
I'm sorry but there isn't a way to check the shutter count within the camera itself, there's no menu option which would display this information. I would recommend sending the camera in to the Canon Factory Service Center (FSC) for the 18-Point Canon Maintenance Service (CMS) which includes checking the shutter count.
You may click on the following link to see a full list of the services offered with CMS. The website will also allow for you to begin online service request for your camera.
https://www.usa.canon.com/support/maintenance-service
If you decide to send your EOS Rebel T5 to our facility for the CMS then please include the following on a sheet of paper and include it inside the box with the camera:
1. Full contact information including return shipping address, phone number, and email address
2. Camera model and its serial number
3. Reason for sending the camera to the facility
With the camera, please ensure you remove all accessories off of it. You will hold on to the battery pack, lens, camera strap, memory card, and if possible, please remove the rubber eyepiece on the viewfinder on the back of the camera. Squeeze the sides of the viewfinder eye cup and carefully wiggle it upwards. It should slide off the camera. Since it's not necessary to include the lens please place the body cap back onto the camera. Wrap the camera in about 3-5 inches of bubble wrap and place it inside a plain, non-descript box. Please ensure there's enough padding material inside to prevent the camera from shifting during transit.
Ship the camera to: Canon Factory Service, 12022 Canon Boulevard, Newport News, VA 23606
