Undersized AC - Options?
I'm not a HVAC expert but a 5 ton unit sounds pretty large for a 3000sqft house.  You can probably approach this in one of two ways.  One is probably what the previous owner did and just throw more cooling capacity at the problem (two units, larger units, etc.).  Alternatively, you can start looking at ways to get more out of your existing unit.  Some things that might help:


Improve attic insulation
Improve attic airflow
If your windows are old, consider replacing them with more efficient windows
Find and plug sources of air leaks - doors, windows, electrical outlets and other exterior openings
Plant trees and shrubs to help shade the house
Install ceiling fans to help circulate the air
Add insulation to the exterior of the house (requires replacing siding usually)
Seal all duct work with proper HVAC tape to prevent leaks
Insulate duct work
Replace your air filter
Install an air exchanger


The benefit of trying some of the above is that they also help when heating.