Remember that with your T5 you will have a 1.6 crop factor to contend with. A 100mm will give you a 160mm perspective...a 50mm will give you an 80mm.......a 200mm will give you a 320mm....etc.,. Crop cameras are favored for enhancing the reach of zooms and for magnification of macros but can be excellent for portraits, etc., too. The problem with crop cameras is that wide angle lenses suffer from also being lengthened....a 20mm becomes 32mm....a 28mm becomes a 45mm...etc., so you lose the really "wide angle" view of some lenses.
The Canon 85mm f1.8 non-L is a very good, sharp and affordable lens that is often recommended for portrait work. You can pick them up refurbished on Canon's website for prices that gravitate around $300 (depending on current sales). I just looked at it looks like that model is currently out of stock. The refurbed lenses from Canon are great deals, though you might have to check all along before you find the lens that you're looking for in stock...they come with a 1-year warranty just like new lenses do. Canon refurb lens link. But, the 85mm on a crop camera results in a field of view equivalent to a 135mm.
When buying Canon lenses, they build them with two different mounts. EF-S lenses are designed for (and work properly) on crop cameras but not full-frame cameras. EF lenses, on the other hand, will work fine on either crop or full-frame cameras. One of the finest crop-camera lenses is the EF-S 17-55 f2.8....very sharp and fast. I keep one on my T2i (550D) all the time. I recently purchased a 6D and I'm using a Tamron 28-75mm f2.8 on it...it's a pretty good lens and seems to do a decent job but I'm looking for something else for that camera...maybe something longer. The image quality of the EF-S 17-55 f2.8 makes it the only crop-lens that I own. Other lenses (I don't own a lot of them) are all EF lenses so they can work on either camera.
Look at the pictures that you have taken and note the focal length that they were shot at...this might point to the fact that a nice, sharp prime might be worth considering. The EF 50mm f1.8 is highly affordable and is a nice, low-light lens....and using the crop-factor of your camera puts you into the 80mm range.
Naturally, moving into the "L" glass class of lenses brings enhanced (most of the time) image quality and build quality...but at much enhanced pricing, too.
Use the camera you have for now, it is quiet capable...as you shoot and start settling into *your* way of seeing and shooting you will start gravitating to the lenses that will work for you style.