Just wondering if I could use two LM7805's in parallel to double the output current
No. Each regulator will attempt to keep the voltage output to its preset value.
So lets consider two LM7805 regulators. There are normal variations between individual regulators.
For this discussion lets assume one output is 5.05V and the other is 4.95V.
You connect them in parallel and the 4.95 regulator sees its output at 5.05V. Now regulators can only supply voltage they cannot remove or lower it. The 4.95 regulator "thinks" gee my output is too high so will reduce my output. Still no change because the 5.05V regulator is taking over. Eventually the 4.95 Regulator shuts down and the 5.05V regulator takes the whole load.
The above explanation takes some liberties it the details of what will happens but I hope the concept is understandable.
Power is a result of both current and voltage. Both must be present to create power.
For a regulator the power will be:
Input voltage - the output voltage = the voltage across the regulator
This times the current will be the power the regulator must manage.
Hope this helps.