First rule of batteries... No battery can deliver what these modern quad motors can pull, but it doesn't matter since you will never be at full throttle for more than a few seconds, and in the beginning you will never go to full throttle since we don't have the experience to handle that much speed and power.
Second rule of batteries... Actual C Discharge ratings are bogus, it is a Marketing tactic, and does not speak to reality. That being said, higher discharge ratings do mean the battery should perform better than ones with lower discharge ratings.
Third rule of batteries... Always get the highest C rating available/affordable. This rule ALWAYS holds true, and don't consider anything with less than a 70C rating.
Forth rule of batteries... Bigger MAH means heavier and bigger size. MAH loosely relates to flight time, and the weight relates to quad performance due to the heavier load it is carrying. At some point the battery gets heavy enough to cancel out any extra flight time and reduces quad performance (due to the extra weight the quad is carrying). It is an option to get a bigger battery if you will only do slow cruising and want the longest possible flight time, but to be honest, I think you get ALMOST the same thing from the smaller/lighter batteries when flown in the same manner. Just as an example, when I first started I could fly for 5-10 minutes on a 1300 depending on the quad I was flying (I have about 10 5" quads), but as I got better, and flew harder, I am down to 3-6 minutes. Once I can push super hard for the whole flight I may only get 2.5 to 3.5 minutes out of those same batteries.
Let's take a look at the specs, and what they are telling us, even if the C rating isn't a completely true number.
1300 MAH (Milli Amp Hours) = 1.3 Amp Hours X 120C (240C burst) = 156 amps continuous with a burst rating of 312 amps for short periods. So that means, if true, the battery can handle your 50.59 amps per motor at full throttle for a short period, and can handle 85% throttle for the entire battery discharge curve.
If this example doesn't answer your questions let me know.
For me, with my experience and knowledge...
I would look at the 1300-1550 size, 1300 is the sweet spot for 5" since it has a lower weight and size, and reasonable flight times, 1550's are about the max size for performance and will yield only another 30+ seconds in the air (due to the extra weight).
I would look at the Tattu Fun Fly 1300 and/or 1550's, they are 100C rated, very reasonably priced, and get good reviews from pilots.
There is sooooo much more to know about chargers, charging, care of your batteries and dangers of them, lowest flight voltage (under load, and at rest), etc, and don't forget, batteries are consumables, they will fail or be destroyed over time. As another example, I have about 200 batteries (from 1s to 6s, 255mah to 1550mah, for Tiny Whoops up through 7" quads), most are 1-3+ years old, and only about 10 have been destroyed or failed on me, so they are likely to last a good long time if properly cared for.
If you do Facebook/Messenger, you should look me up and send me a friend request. I often use Messenger to talk and video chat with friends (many on this forum) that are out of the continental US for free. In this way I have helped about 50 people globally to date learn the basic ins and outs of the hobby. Below is my FB Profile pic so you will know it is me, the account is under "Randall Harbin" (aka fpv-fog). If you do send me a request, you will need to let me know here since I get about 10 per day and I won't know which person is you since I don't know your FB name.
