My iMac won't let me upgrade my flash player.what can I do?

I have a Mac OS X version 10.5.8 processor 2.66 GHz Intel core two dual 4 GB memory with a Macintosh HD start up disk.it tells me I need to upgrade my flash player. When I download the upgrade it keeps going and to read launch every time I try to open application.what can I do to alleviate this problem and get my flash player upgraded?