Minimum...
 

What's the minimum voltage for a rx7 to start?
I have a battery that's giving a little less than 13 volt with key on...
engine just keeps on spinning until the lights dim...
probably needs more voltage no?

No.

what could be the problem??? My engine just keeps spinning until the battery almost seems to die...that's only 5 seconds....

Fuses, electrical, fuel problems. Check the simplest ones first.

If you sit there and try to spin a dead engine for 5 seconds, it will drain the battery eventually.

That's totally normal battery voltage with the engine off. There's some other reason your motor won't start - fouled plugs, flooded motor, general problems with the fuel injection system.

Dale

last time i had the same problem i took my battery and went to a garage..they charged the battery until i got 13.5...came back home and the car started...
I still believe it's the battery...can somebody confirm?
My car sits in the garage for the whole winter time. and i start it once a week but very shortly....i kill the battery when i start only a couple of seconds...do I?

also whenn i press on the brakes...the dome lights becomes very dim...or even blinks..

Sounds like you did a good job of flooding it. :D