'90 Auto Transmission slips

Once the car gets warmed up,(after about 15 minutes) the transmission takes a few seconds to get out of first. It'll rev pretty high (4-5k rpms) and then eventually will shift... Do I need a new tranny? Or can this be fixed less expensively? Thanks for your help.

This sounds very similar to my problem. See my post "Opinion Please".
I hope it's something simple for you!