I can make two recommendations on your T case, the first being to change the fluid in it if it hasn't been done lately. I recently did mine with Royal Purple and the improvement in t case shifting was amazing.
Second, are you moving at around 4 mph when trying to engage 4lo? It won't want to go in when you're stopped.
A third thing that could happen is the t case linkage might need adjusted. I had the same issue as you not too long ago and doing that fixed it. I kinda had to do it twice because you need to be in 4lo to adjust it, so I adjusted it until I got enough play in the lever to get into 4lo, then adjusted it again from there.
Are you burning oil or leaking oil? Mine used to leak a bit until I did my valve cover gasket.
Also personally I use 10w-30 (non synthetic), 5w is a bit too thin in my opinion unless it's reallllllllly cold out, like into the negatives. So if it's thin maybe that's why you're leaking so much?