Over loading?

My 5250 says - Current Capacity 45 amps peak per channel, x5.
The 2003 says - Current Capacity 60 amperes peak, per channel, x3.
Correction. 405 total.

Darn if it doesn't say 60 amps peak per channel. Somebody smarter than me will be along shortly but if it was an issue it would have a 30 amp plug. There are very few amps that require 30 amp service. I have had amps that will dim the lights with each beat of the music but I was very young back then and don’t do that stuff anymore.

So the 5250 =  250 watts x 5, 8 Ω / 385 watts x 5, 4 Ω.
The 2003 =  200 watts RMS x 3, 20 Hz - 20 kHz, 8 Ω, all channels driven  300 watts RMS x 3, 20 Hz - 20 kHz, 4 Ω, all channels driven.
So which do I go by? 8 or 4 ohm?

The peak current value of an amplifier is the maximum amount of current which output is capable of sourcing for brief periods of time.
Instead, you should look at the maximum power consumption specs to determine if a 15amp line is sufficient.
For 5250, the maximum power consumption is 2500watts,
the 2003 maximum power consumption is 1320watts.
2500watts / 120volt = 20.8amp
1320watts / 120volt = 11amp
It is best to run each amplifier on separate 20amp and 15amp line if you drive them to maximum rated power.
However, unless you use them to drive very low efficiency speakers in a very large room with high volume level, I believe it is OK to use a single 15amp line to both amplifiers as long as they do not tripping the circuit breaker.

+1 imhififan - I concur with everything he said. For me I changed my 15 amp breaker to 20 amps because it popped occasionally on power up only, never while playing loud. I had 9.6kW output into 4 ohms though...