Do you mean this. Is it actually better than buying the original off Amazon?

I don't really know much about rooting (I assume that needs root?), and warranty is already long gone. Should I really look more into that for a phone of this age?

If you are going to buy one of these, make sure you know that you won't be able to use NFC if you dont get their NFC capable version for 4 dollars more. link

Anker is top notch.
 

They used to sell a two pack of batteries on Amazon but seem to have removed it, now all that seems to be available is the single S5 battery - https://www.amazon.com/Anker-2800mAh-Battery-Samsung-T-Mobile/dp/B00N8ULV7K/

The two pack of batteries with the very handy travel charger seems to be available from the Anker website - https://www.anker.com/products/70SMS5-S22P1NA

 
My son and I have the Tmobile S5, both going strong and the Anker batteries are every bit as good as the factory OEM, if not better.
 

I did a day long write-up on my Anker battery life a few months back, its here if you want to see it - https://www.reddit.com/r/galaxys5/comments/4s3u0j/how_long_does_your_battery_last_nowadays/d5894a1/

I'm on Stock 6.0.1, G900A. I went from 1.5-2.5 SOT with the OEM Samsung battery after 13 months of use, but then bought the replacement Anker battery from Amazon for like 8 dollars and now have 3.5-4+ easily. Lasts me all day unless I use maps/location services/etc. along with heavy multitasking.

Sounds you may just need a new battery.

EDIT: I believe it was this one. Pricier than I remember, but definitely worth it if you are on a year or more on your current battery.

https://www.amazon.com/Anker-2800mAh-Battery-Samsung-T-Mobile/dp/B01LY08DAA/ref=sr_1_1?ie=UTF8&qid=1487792878&sr=8-1&keywords=anker+galaxy+s5+battery

EDIT 2: Seems that the battery I bought specifically is unavailable, so the one I linked in the first edit is a newer one by Anker.

The one I bought last year: https://www.amazon.com/gp/product/B00N8ULV7K/ref=oh_aui_detailpage_o03_s00?ie=UTF8&psc=1