Audi's Dad

I have a 97 Cabriolet I am rescuing and have all the mechanical issues worked out, on to other matters cosmetics and sound. So after discovering that both my rear speakers were done I started looking at replacing them. Turns out Nokia OEM speakers are around $270.00, I am assuming because they have a built in 20 watt amp built in. I would like to purchase a mid-priced pair of 5.25" speakers and use a pair of small 5amp.50w amps that run around $15.00 placed under my back seat utilizing the existing power and audio wiring from my speakers. I have $5.00 hearing and can't justify $1000.00 audio set-up in my car, I just want to listen to FM radio and my old school R&R cd's. Does anyone see a reason this won't work. Any advice would be appreciated