Wifi router setup Question regarding amperage/voltage drop
Using 'official data' to check Tom's back of envelope figurings.
Alas, Frank's mental magic was very close to actual.

Wikipedia Cat5e data here

Resistance = 0.188 Ohm per loop metre.
275 feet = 84 metres 
84 x 0.188 = 15.8 Ohms
Two parallel pairs = 7.9 Ohms -> say 8 Ohms.

At short circuit I = V/R = 5.25/8 = 0.66A.

To get 3A over this feeder at say 0.5V drop needs
V = IR = 3 x 8 = 24 V 
So total feed voltage needs to be about 24+5 ~= 30 Volts. 
Of the 90 Watts input about 85% is dissipated in the cable.