You really should not buy that "extended" battery. There is no way it can possibly have over 5000mah capacity and be the same size as the stock 2800mah one, if that were possible don't you think Samsung would have made it that way in the first place? Think how many more phones they would have sold as a result-
By the laws of physics and how battery chemistry works, if you want to increase the capacity of a rechargeable battery by a significant amount it HAS to be physically larger. There are no exceptions, not even on Ebay.
If you are dissatisfied with the battery life on your S5, especially if you bought it used, it's very possible the original battery is weak and needs to be replaced. Remove the battery from the phone and visually inspect it, if it's at all swollen (see if it sits flat on a table or if it rocks/spins) it must be replaced asap. If that is the case replace it with a new OEM one, preferably from a store that is an authorized Samsung dealer as there are a lot of fakes selling online.
Beyond the battery itself, there are plenty of things you can do on the phone to help with battery life most of which are common sense. Keep the brightness down to the minimum level for visibility, turn off any radios you don't actually need (Bluetooth, GPS, wifi), look at what's running and disable apps or services that are constantly using background data. Some apps such as Facebook are known battery hogs, do some research and get rid of these if you can do without them.Turn off things like push notifications that aren't necessary. And so on.
I do not have an issue with the battery life on my S5, and if you follow the above advice you may not either.
Another option if you still feel you need more run time is to pick up one of the many external battery packs that are available, you can get one in the 5000mah range that can easily be carried in a pocket or laptop/accessory bag.