Im not an expert here but I would recommend to choose a high discharge rated battery .....20c discharge is not good enough.
i think you should go for any battery above 35 c discharge...
good luck with your project......and show us some pics too....
firstly decide on a frame as it is a major weight contributor.
just a few points. 5000mah battery is heavy and will add to power consumption rate.
instead you can go for two smaller batteries.
if you are targeting for a quad over 2kg then i think a 4s will do a better job or you will need to increase the size of the propeller to either 11 or go for 12 inches. a quad of that weight will start hovering at 40-50% throttle with 10*4.7 props.
also i'm saying this because i don't know what you're going to use it for... but the JST to 3x2mm bullet connector is designed to work with a
10Amp multistar ESC.