The 7805 is an old design, one of the first 3-terminal regulators. That's not automatically a bad thing, but it does mean that the part is not very friendly, and designed for specific uses that are relatively narrowly defined. Specifically, it does not current share well while maintaining decent regulation. If you add ballast resistors and an external opamp you can treat two of them like pass transistors, but that's a lot of work for something that can be done with a $1 part like an LM350.
ak