T5i video quality doesn't even match smartphone camera? Where can I improve?
Bottom line with the canon rebel series cameras is that the video is pulled from a low resolution capture of the chip which is normally used for high resolution photos. The photos from these cameras will resolve many thousands of lines but the video compression chip in the camera cannot deal with these in real time so they just grab the image that goes to the rear LCD screen.

This image is achieved by throwing away the high res photo lines (or pixels), this is called binning (discarding). This makes high contrast edges very aliased or have a stair stepped effect. To fix this Canon soften or blur the image to make it more acceptable. Guess what, all of this results in a video image that ends up resolving at about 480 vertical lines or standard TV resolution 'not' HD resolution. So no amount of sharp lenses or post sharpening will ix the matter. The soft is baked in.

While the phone camera is built specifically to capture a fixed line resolution but it compromises on maximum photo resolution, typically not better than the video resolution.