Is it legal to have the air intake (for heater and ac) coming from outside in CA

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.

The air handler, blower, is designed to blow a certain amount of air over the cooling coils which in turn converts the refrigerant back to a gas from a liquid. It can only get the correct amount of air if all the returns and supplies are installed, otherwise the blower will not function as designed and can ice up the coils. This affects the compressor operation as the transformation of the refrigerant from gas to liquid back to gas is compromised. If the outside unit has to be charged or topped off if it's a precharged unit, everything needs to be running correctly to get the right refrigerant charge in the unit.