When trying to start the mower, it acts as though there is too much compression. Once I click the started 4 to 5 times and it makes about a half rotation it will then take off. A friend mentioned to me that the valves may need adjusted. Is this something that I can do or should it be taken in to a small engine shop?

Compression does not increase over the life of an engine. It sounds more like the starting system is having problems overcoming the existing compression. The good news is that the ignition is great since it starts on half a rotation. Forget the valves. Suspect a weak battery or possibly a dragging starter. The likely suspect is the battery.

I am not sure for your engine but many have a valve that lowers compression during starting. If your engine has this it may be malfinctioning. Just a place to start looking. Here is an old thread discussing the topic https://www.askmehelpdesk.com/tools-power-equipment/20-5hp-briggs-compression-release-valve-89671.html

Don't know if you got this problem fixed but I have an old Murray had the same problem seemed like the starter was bad it would only crank a second or two. Got a set of feeler guages and opened front cover on engine and adjusted the valve lash. Started up like majic! Can't remember where I found (Googled it?) the valve lash setttings. Hope this might help