This question is right up my alley. My daughter skates with a local club and now at the level where she earns solos in the annual ice show, she has her Axel and several doubles in her repertoire. Shooting ice shows is the reason that I invested in my 70-200 f2.8L II. It's also the reason why I upgraded from an XT to a 60D, then a 7D, and now a 5D3. A 1Dx would be great, but frankly the 5D3 is filling my needs quite well.
Your T5i can handle this, but if you are going to rent, rent a 5D3. With either body, your ISO will be between 1600 and 3200. I will often go beyond.
Whether its your T5i or a rented 5D3, get to know the camera. Know how to change settings and how navigate the menu before you get to the rink. Be prepared to trouble-shoot an errant setting and to change a shooting mode in a hurry and in the dark.
Lightroom 5 is great for noise reduction. You need more with the crop body than the with the 5D3. Shoot RAW.
The key is to get lots of practice. I assume that your rink is built for hockey. The best vantage point is the players box. It gets you at ice level and you avoid the plexiglass. The 70-200 on the 5D3 has great range from this position. I typically shoot in landscape. With a crop body, things can get tight when the skater gets close forcing a vertical shot. I use a monopod with a Manfrotto tilt head and quick release. I use the collar on the lens and the tilt head on the monopod lets me tilt up or down. The collar gives me the horizontal to vertical option.
Shutter speed will vary with the talent of the skater and the action on the ice. 1/200 minimum for younger skaters and spirals. Pan with the skater when you shoot. For rotational jumps, 1/500 is minimum. When I shot with the 7D, I was at first afraid to go beyond 1600 and often lived with shutter speeds of 1/320-1/500. Today, I typically shoot 1/500 to 1/1000. A sharp noisy photo is better than a blurry clean one. It's easier to clean up noise than blur.
With my 70-200, cropping a shot from the 5D3 is sharper and cleaner than one from my 7D.
With the 5D3, I shoot with high FPS setting, AI SERVO, spot focusing with 8 expansion points, AF Case 2 (yes, I prefer this over Case 5 which is for erratic movement), back-button focusing, spot or partial metering, manual mode, RAW, AWB, f2.8, shutter 1/500-1/1000, and ISO 2000-4000.
Regarding the IS on your lens, leave it on. Above 1/500, it may not help, but it doesn't hurt and it will help if you must go lower. Lately, I shoot a lot at 1/1000 with it on and off and cannot say that I've noticed a difference. The biggest problem with turning it off is forgetting to turn it back on when you need it, like with a shot backstage.
Anticipation is key. Shoot during practice so you know the routines and practice your timing. Unless you use a 1Dx with 12 FPS, do NOT rely on spray and pray to get the shot. Even with the 8 FPS of the 7D, burst mode is no substitute for timing. Surprisingly, I am more likely to burst during a slow spiral than a fast jump. With the spiral, I'm looking for background and little happens between frames. With jumps, a lot can happen between frames at 8 FPS. Split jumps are often the best to shoot because you can get some hang time at the peek of the jump. I do often burst a couple frames when I try to get the apex of the jump (sometimes due to a heavy finger). This is what you want to shoot. For rotational jumps, get the take-off, try to get the apex, than the the landing. Single jumps are tough. If the skater is facing you during the take-off and landing, they then face away from you during the apex of the jump. Just about ever point in between these can be very unflattering.
The 7d and the 5D3 are great for tracking the skater. Use AI Servo. But understand how it works. It keeps track of movement to predict where the subject will be when you trip the shutter. Skater's change direction frequently and can through off the AI Servo. This is a bigger problem for Rebel's than the 7D and 5D3. To get around this, get in the habit of lifting your finger off the shutter briefly when the skater changes direction. I assume that you are "riding" the shutter (or back focus button) to track the skater. With AI Servo, ride it, that is, be sure to pre-focus for at least second before shooting. This gives the chip more info to predict the focus when the shutter trips.
The other issue that you will run into with the 5Ti is it's buffer. Even if you aren't bursting lots of shots, you can still shoot a bunch in a hurry and fill up that buffer. The key here is to know the routine and don't fill the buffer getting the take-off to a jump. Save a couple frames for the apex and landing.
Again, practice, practice, practice. Practice to know figure skating so that you can see when a skater is getting ready for a jump and zoom so they don't jump out of the frame. Watch for sit spins, skaters often go into a standing spin and out of your frame if you are too tight. Practice timing spins. Practice to learn the routines. Practice to learn the limits of your camera. If there's a dress rehearsal, this can be your best chance to get shots and to learn how the lighting will be.
Figure skating is about the skating. Full body shots are often best. Save the closeups for ending poses.
I prefer to shoot in manual mode and pick an ISO that supports shutter speeds of 1/1000 when all spot lights are on the skater. I then bump the shutter speed down when fewer spots are on the skater. Chimp a lot so you know that your exposure is in the range. You will get to the point where you know what shutter speed to use with 4 spots vs. 3 vs. 2 vs. 1. I don't like auto exposure because the background and or the costumes are rarely 18% gray.
I must note that I have had a lot of good luck with 1/500. It all depends upon the skills and speed of the skater.
Check out this link for more detail. Scroll to the bottom for a complete write-up on shooting ice shows. This was written after a show in 2012 that was shot with a 7D -- before any experience with the 5D3.http://www.skatetheoval.com/page/show/281573-photo-gallery
This link includes exhibition galleries. Those after April 2013 were shot with the 5D3. Sorry, don't have the 2013 or 2014 show photos posted here. But, the 2012 show photos are.
Here is a gallery of shots from the 2012 show shot with the 7D. Shutter speed range was typically 1/250-1/640 with ISO 1600-3200 -- maybe half at 1600 and half at 3200.http://www.skatetheoval.com/photo_gallery/show/580178#1
Hope this helps.