Reviews that may be worth reading:
Canon Rebel T5i vs Nikon D5300
Snapsort Canon Rebel T5i vs Nikon D5300
Camera Labs review
The Nikon D5300 has a larger image sensor (23.5 x 15.6 mm) than the Canon T5i (22.3 x 14.9 mm). The Nikon D5300 also has a smaller crop factor (1.5x) than the Canon T5i (1.6x).
Crop Factor Explained
The Nikon D5300 does offer more frame rate options than the Canon T5i:
D5300
@ 1920 x 1080: 60 fps, 50 fps, 30 fps, 25 fps, 24 fps
@ 1280 x 720: 60 fps, 50 fps
@ 640 x 424: 30 fps, 25 fps
T5i
@ 1920 x 1080: 30 fps, 25 fps, 24 fps
@ 1280 x 720: 60 fps, 50 fps
@ 640 x 480: 30 fps, 25 fps
From everything I have read it appears both cameras are equally matched regarding video quality.
The Nikon also has a less shutter lag (200ms) than the Canon (264ms).
I have a Canon T4i and I like the quality of the video I have shot with it. Canon quickly replaced the T4i with the T5i and one of the major improvements was a better kit lens along with some other changes (though looking at the specs they are very similar).
I know I didn't give you a definitive answer as to which is best but hopefully the information provided will help you make an informed decision.