The Arduino should not be powering anything and certainly not motors requiring 12V 5A, it is a controller, not a power supply. The motors should be powered from the battery and controlled by the Arduino.
You say you have a 12V 5A battery, I think you probably mean a 12V 5Ah battery. The 5 relates to the storage capacity of the battery, not the amount of current it can supply. It means, for example, that it would be able to supply 2A for 2h30m or 0.5A for 10h. Whether it can supply the possible 10A of the 2 motors is another question.
You can't use breadboard to connect motors requiring 5A, the contacts are not capable of carrying that much current, they will probably get hot and melt the plastic.
It would help to have links to the actual battery and motors you bought and to their data sheets, and a schematic of how you propose to wire them up.
This was actually really helpful and I think this helped me solve the issue/come up with a solution. After some more research I believe adding in a sabertooth 2x12 motor driver is going be the solution. I’ll be able to connect both motors to the driver as well as the power source for the motors and then connect that to the Arduino. Should help me avoid melting down the breadboard and the Arduino.
this SCREAMS for a simple schematic.
hardware questions and schematics go hand in hand
The motor bit is simple, if we had a clue as what you are doing.
post a link to the motor spec sheet, or where you bought it or some such.
Battery will always be an afterthought. it really doesn't matter at this point.
if it drains too fast, there is only 1 solution, get more power. there is no big discussion there.
Motors usually need a driver. ( the Arduino is the controller)
The driver handles ALL of the high power and high voltage.
The Arduino controls the driver with very low power, 5v signals and never sees the high voltage.
Driver module if you need speed control, relay module if you do not. One relay for single direction operation, two SPDT (usual sort of) relays per motor for reversing.
There is ONE more motor specification that is not given that may kill you design. That is the current needed at the instant the motor is started. It may be many times the "load current", which is the current AFTER the motor is turning.
Paul