A stock 7805 can’t convert 5.1V to 5V ... The schematic notes you can also replace the IC with an MT2492. With a right-angled header, you can swap the board in for a standard 78XX.
Finally, [Ken] takes apart the LM7805 voltage regulator. The output transistor is (not surprisingly) about half of the IC die — the 7805 needs to push some current. The coolest part of the chip ...