need a small but powerfull audio amp

Im trying to build a small solar powered boombox [currently i have a 4.8volt 3.4AH battery so a battery life estimate would be nice] i have 2 5 watt 8ohm speakers and a 30 watt 8ohm sub and i am trying to find a suitable amp to drive them from an mp3 player. Im looking for something as simple as possible without sacrificing sound quality. [also try to keep it under $20 ]

4.8V is not sufficient for a good power amplifier. Think about 12V.

look into class D amps into 2 or 4 ohm speakers... even class Ds will not put more than 2W into 8 ohms at 5V

many cars speakers are 4 ohms...

I can get it to 12 volts without much trouble i have about 1000 AA NiMH batteries ive been building my own packs out of.

You could saw off apart the output amplifier section from an unwanted car radio with a hack saw, leaving the portion of printed circuit board near the output amplifier modules and a piece of chassis for heat sink. If it is a 4 channel, one could be used for the subwoofer and one spare. Look at the part number for the amplifier module and its data sheet will tell how to connect inputs and power.