Chithra,
I have the same phone, and have had the same problem. I initially tried syncing my phone with iSync, but it wasn't supported. You can get a 3rd party driver from here:
http://pyxx.org/nokia-5310-xpressmusic-isync-plugin/. That allows you to sync using iSync (iSync will recognize the 5310 as a valid cell phone).
However, although the phone is now supported, I try to sync the phone and get the following error messages:
"There was an error getting data from the phone. The synchronization may have been canceled on the phone." (from iSync)
and
"Data transfer not possible. Check data connection." (from the phone)
As a disclaimer, I obviously didn't cancel either process; It simply stopped after awhile gave me those error messages. I'm assuming it's a problem with the driver, and I'm going to contact the guy who created it. It could be just a problem with my phone. Anyways, hoped this help.
-T