It really does sound like you have a leak, and you want to find and fix that before you hook up another tank. Spray on soup water to all the connections, you should be able to spot a leak quickly. Also check the rubber seals in your connections, make sure you have them, and that they are not torn, or worn out.
Best of luck, CO2 can get expensive with a leak. I can go well over 10 kegs with one 5 lb tank, and I still have not had to swap out my 20lb tank in my keggerator yet.