Well, that amplifier will put out NO WHERE near 5000 watts. It won't even put out 2500 watts...EVER. NEVER NEVER NEVER pay attention to peak wattage, always look at RMS or continuous wattage. According to specs, you amplifier SUPPOSEDLY provides 1750 watts rms @4ohm bridged...but i HIGHLY doubt that even! (especially at the price of $155).
BUT, as stated...use AT LEAST 4guage and upgrade your alternator to battery wire, the battery ground to chassis wire, and battery ground to engine black wire. Also, look into replacing your stock battery with an optima yellow top. After all this, if it hasn't stopped, or decreased significantly...then you should look into an alternator upgrade.
Also, just to address this at the beginning...DO NOT get a capacitor (cap). It's a bandaid for a weak electrical system, and it only creates another load on your already strained alternator!
Good luck, peace.
NG