Hard Starting After Warmed Up.....Arrrg

Well, after a 30 minute run. I let her sit for about 30 min. I started her up and she was still a lil slow to start (about 3-5 seconds) . She slowly started up and ran fine.
I guess I'll have to live with it for now.
I was hoping she would pop right on the turn of the key, but it may be because it's an older motor and thats the way it is for now.
Any additional input would be appreciated. I am wondering if it's the old original starter itself. But I am not going just throw money at it for something that it may not be.
I could use a new starter anyway. I know this is the original starter that came with the car.
I have a 360 thats in the works by a member here. Once i swap out the teen for the new motor all will be good.
I appreciate the help.
Always glad to learn something.