Like others have said. That's a lot of propane, and you should be smelling the leak. The only place I can think that it would vent where you would not smell it is up the fridge vent.
OK just be clear....i am NO LONGER LOSING A TANK IN 5 DAYS. i did smell, find and repair that leak.
i am losing the contents of the lines in 6 hours. NOT A whole tank. I pressurized the line then turned off the tank. 30 mins later i still had gas, an hour later i still had gas. 6 hours later no gas.
You will not have a perfectly sealed system- the standard is for the system to hold an 8" wc reading for 3 minutes with no change in pressure (8" because the test is commonly done at the stove, which is regulated to under the 11" wc, plus to make sure the service valve is not leaking). With the modern solenoid valves, you will have some leaks- they just are small enough to be no danger.