What are the best lenses for outdoor sports for the EOS Rebel T5?

[Astron01]

I'm trying to figure out how can I find the right lenses and other accessories for outdoor sports action photography, so I was wondering if there were any suggestions. I want these photos to look professional for my portfolio.

[kvbarkley]

Any telephoto "L" lens will work, to be more specific we need to know:

How far are you from the action?

What is your budget?

[Astron01]

Don't have one currently, but I can show you examples of the action photos you're talking about.

[Tronhard]

The first thing you need to establish is a budget.  Unless you have very deep pockets, then you have a limit for what you will buy and establishing that will assist you and us to limit the choices to ones you will be able to afford.

Outdoor sports can cover a lot of territory, based on the type of sport you are considering, and how close to the individual players you want to shoot.   There are some excellent videos I posted from Brigham Young University on shooting various types of sports:  they might be a useful reference for the types of images that are captured and also the focal lengths they use, even if you can't afford their budget:

If you follow their videos, you may find them quite instructive...  Baseball may have some similarities.

As an extension from that, I would consider the following:

For relatively shots of relatively close by subjects, I would consider the EF70-300 f/4-5.6 MK II IS USM.  This is an excellent lens at a reasonable price with image stabilization, blazing fast focus and good optics. 
EOS 60D, EF 70-300 f/4-5.6@86mm, f/7.1, 1/200sec, ISO-200
See my article : A Review of EF 70-300mm lenses 

If you want even more shallow DoF, then go for a EF 70-200L MkII f/2.8 IS USM.  Heavy duty professional-grade lens with great optics and offering excellent low light performance.

If the action is further away, then something like the Sigma 150-600 Contemporary or the latest Tamron equivalent. Both these lenses offer long reach with great optics for a reasonable price.

Finally, the L lens for this range is the EF 100-400L MkII, which is not cheap, but fabulous optic and built like a tank.

The longer lenses can be challenging for some to hand-hold for extended periods, so a monopod would be worth considering, like the iFootage Cobra, actually designed for video but brilliant as a shooting platform: Cobra 3 - Pedal Version – iFootage (ifootagegear.com).

You will want batteries, good quality FULL SIZE SD from reputable vendors like Lexar, SanDisk and Prograde, cards that are fast.

[ebiggs1]

"The first thing you need to establish is a budget."

Perhaps, but a better and more logical place to start is to know or find out from where you will be shooting. This is by far the single most important thing. You can figure a budget for sure but that number can be affected by your shooting location. And, of course side lines or on field is best . Secondly the next step is to know the sport. Not knowing or understanding what is going on and what is about to happen is going to be a problem and the best gear in the world will not help. Knowing these two things, now create a budget or how much you can afford. Remember the better lenses are going to cost more a lot more in most cases.

But even before we get to the lens I am going to recommend there are two more things you need to do and both are free as were the previous recommendations above. D/l, DPP4 from the Canon web site and always set the T5 to use raw files never jgp. DPP4 will u/l and convert your raw files to your computer to allow you to do some light or extreme editing, your choice, and make social media photos.

So here we are location, learn the game, DPP4 and raw. All free! My go to lens of choice for your T5 is the Tamron SP 150-600mm f/5-6.3 Di VC USD G2. It is likely the best all around outdoor sport lens available for a Rebel DSLR today, performance vs cost. It is big and it will require you do your job to learn how to use it but if you do it will get the job done. Last question, does it fit the budget?