Why won't my 2004 Toyota Avalon go into drive but goes in reverse.

Sure, your transmission could be malfunctioning. It took 5 quarts of fluid? That would be mean the transmission was extremely low in fluid, if the fluid is now at the proper level. Will the fluid help at this point? Maybe not; if the fluid was low for a period of time, there could be internal damage related to this. Either way, a diagnostic tool capable of monitoring transmission system operations is needed so you can see what is being commanded and what is actually happening. Testing from this point is what needs to be done; seek guidance from a local shop near you.