Kevin Miller 1964

Hello my name is Kevin and I am not sure if I am posting in the right place or not. I have a 2005 Chevy Impala with a 4T65E transmission and 3.4 engine base model. My question is and I appolagise if it is posted somewhere else I have a problem with my trans not shifting when it is supposed to. It does shift and not what I call slip but it takes to long for it to shift. You can hear the engine race before it shifts in gear. It is an easy shift not harsh. I bought this vehicle used about a month and a half ago from a lady who bought it from someone and noone really knows how it was maintained. I am really hoping I dont need to have the trans rebuilt. My question is could it be the pressure control solenoid going bad? I heard these vehicles are known for that issue. Also there are no coded stored in the vehicle everything is clean with a code scanner. What are my chances be of it being a pressure control solenoid? Yes there are high miles on it with 236,000 however it runs like a new engine with no oil consumpsion and a very smooth idle. Any suggestions I would very much appreciate it. Thanks for taking the time to read this story lol.