Ok lets look at the math
amps are equal to watts divided by volts
The roll you are looking at only has a total of 296 LEDs for the 4 meters. Each LED is just over 1/2 apart. Each meter is 17.76 watts running at 5 volts so that's about 3.5 amps. now with 4 meters that's a total of 14 amps per roll. The rolls were designed to run that amount of power. The amps sounds like a lot but remember it only 5 volts. Think more of the Watts. These lights are individual LED with each having its own chip. that means you can cut in between each one. The same strip at 12 volts you can not. There are 4 chips on the back side that reduce voltage on those. Once you cut a strip just fill in the end with a silicone caulk. I have done that for years. I'm using the a similar strip that's 60 LEDs per meter for my Ferris wheel. I'm cutting every 34th LED and soldering wires on to feed the data through to the next section.
When trying to determine the proper gauge of wire, you're mainly concerned with the AMP (passing through the wire) and DISTANCE....that will determine the necessary GAUGE. Assuming proper insulation, VOLTAGE (and therefore WATTAGE) don't necessarily factor into the equation. There are plenty of reference available to help with this:
https://www.bluesea.com/resources/1437
14 amps / roll is significant, so it's a valid question/concern. You don't truly have 14 amps *going through* the entire roll...but it is recommended that you provide power from both sides (if using a full roll, and not cutting/sectioning).