I need 5v@500mA to 12v@5A for 2.5 seconds every 5 minutes
At 12v at 5 amp, for 2.5 seconds, you need to store 150 joules.

At 100 volts across a capacitor, the formula 

Energy = 0.5 * C * V^2

may guide you. 

A one farad cap at 100 volts holds 5,000 joules. Thus you need about 0.03 Farad cap.