Will a subwoofer fix my problem?

I havent read what everyone suggested but I can say from experience that my 5.25 speakers are deffinitely pretty bright. You can adjust the gain and the x-cover on your amp and that should help some. Also, if you are using a component set, try mounting the tweeter so it dosent face right at you. That can make them sound bright as well.

Adding a 12" sub will compensate for the lack of really low frequency sound and sould make an imporvement. You wont notice a huge difference in midbass though which is what I think you are lacking in. Play with your settings on the amp.

If all else fails, I am using a set of Infinity Kappa perfect 6" 2 ways. They are much more full sounding thatn my 5.25s.

Your only solution for what you want is a subwoofer. Go with an 8" or 10" sealed sub if you want nice tight bass that isn't huge. To bring the block down go with a 10" to 12" ported setup (tuned correctly of course)

Same prob with my buddies 93 cobra, Infinity speakers all around with components, sounded nice but no bass (of course)
2 10's in a sealed box and an amp, nice fill and not too bass'y. Your not going to get good freq. response on your lows with little 5.25 speakers, and the coaxil speakers in the back are just for rear fill, they wont produce any bass. Get some subs and you'll be happy, even one 8 would make you happy