Evaporator Coil Cold, but Not Ice Cold
You never want the coils in the evaporator to ice up. Ice can damage the coils and reduces the airflow. More often I find dirty coils outside many times filled with dust so they are not cooling the refrigerant.  A 5 degree delta sounds small but is meaningless without the air temp , with a system this old an 80 deg outside temp you should be closer to 15-20 degree drop. 
My guess would be that you are low on Refrigerant so the system doesn’t have the volume of high pressure liquid to be released and create the cold you are used to. You probably have R22 and it is Running ~100$/ lb , I have heard higher in some areas but it can still be purchased a 5 ton system may take ~ 8-10 lbs to bring back to full cooling, and they will probably try and talk you into updating to a new refrigerant basically a new system.