Stock 5.0 Auto Transmission Hard Shifting??

I have a 88 GT with 115K on the stock engine and transmission. The shifting is fine when you are barely on the gas, not romping but steady even gas. When slowly moving to the speed limit though it shifts hard into the next gear and sometimes strains trying to get to the next. I have rode in a 99 Beetle that does the same thing, kinda slamming into the gears on its on since its an automatic.

Any thoughts as to what this is? Is the transmission going out? slipping? an easy fix.. maybe a part in the transmission, etc... Keep in mind I am a banker, not a mechanic. So i only know laymans terms...

Thanks yall!!!

I am taking it to a Ford Performance shop this week to get a valve gasket replaced, so i will ask them, i assume they will know... Thanks for the help!!!