As Ernie points out... the computer merely tells the camera when to take the shot. If the camera has a flash, then the camera will trigger the flash when it takes that shot.
But your question is loaded with some nuances and it's not just a straight-forward answer.
A Canon T5i has the ability to remote fire a Canon speedlite if three conditions are true:
1) The flash must support E-TTL
2) The flash must support E-TTL "slave" mode (and that mode must be enabled -- it will not be enabled by default.)
3) You must have a direct "line of sight" between the camera and remote flash.
The camera itself has to be told that it is in a mode where the on-camera pop-up flash will work as a "master" to trigger a remote flash.
But you mentioned that you wanted to place this remote flash between a subject and backdrop -- implying that "line of sight" may not be possible. That calls for additional gear.
You can learn a tremendous amount about Canon E-TTL flash systems from "The Speedlighter's Handbook" (by Syl Arena) but that book hasn't been updated (so far as I know) to include Canon's new radio-triggered flash systems.
To do this with Canon gear, you'd want an ST-E3-RT radio transmitter (that mounts to the camera hot-shoe just like a flash) and then use a Canon Speedlight flash with an "RT" suffix such as the Speedlight 600EX-RT (the flagship flash) or the new 430EX III-RT. All the "RT" products communicate via radio and do not require a direct line-of-sight.
It's also possible to do this with budget gear... you can get a pair of radio trigger transceivers... one goes on-camera and the other goes with the remote flash. These radio triggers are not "E-TTL" which means the camera and flash will not be able to communicate to negotiate how much power should be used for the shot "on the fly" (as an E-TTL flash can do). That means you'll have to manually set the power level you want to use.
Having to use manual flash is not to terribly difficult to learn. The flash and camera wont automatically set your power level as it would for E-TTL flashes. You control the light by adjusting the power level on the flash (manually) or by moving the flash closer or farther from your subject (or by using light modifiers on the flash) or by adjusting the camera's aperture.
This works well in a "studio" type situation where you can control power settings. But for "event" photography where you have to shoot on-the-fly and don't get "do-overs" if you botch the shot, you have to learn the flash behavior before you do the shoot. For me, this meant creating a table that shows (for any given power level on the flash) what f-stop I should use at any given flash-to-subject distance. I typically used non-zoom lenses back in those days but I knew that, for example, a "dance" shot of a couple from waist-up (what we called a "half shot" because we only include the upper-half of our subject's body) was f/16 at ISO 100. A 3/4 length shot (basically from the knees up) was f/11. A "full length" shot was f/8, and a group shot might be f/5.6 or even f/4.
This required some quality time spent testing and filling out such a table. You wont have time to reference such a table, but I mentally memorized it by distance because subject framing was a good consistent indicator of distance. (this is a bit trickier with zooms because you can change the subject framing without changing distance.) But ultimately you end up in a situation where you walk up to a subject at an event, frame the shot, set the f-stop, and capture the image and know that you nailed the exposure even though the entire system is manual.
There are lots of tutorials on how to use manual flash and inexpensive triggers at the Strobist blog (strobist.blogspot.com).
I use the Canon system. I use the Canon ST-E3-RT trigger a couple of 600EX-RT speedlights. The system is rock-solid... it always works.
Tim Campbell
5D III, 5D IV, 60Da
