You are correct that even with the higher than expected input voltage, the output should still be 5V. The reason for the higher voltage from the wall wart may be that it is an unregulated type. These quite commonly will deliver a higher voltage than their nominal rating, especially with no load or low loads.
Reasons I can think of for the 8 volt output:
- You have a 7808 instead of a 7805
-- If the output is very close to 8V, then I suppose it could be a mislabeled part but that would be very rare. - It's a defective part. Not common either, even from Radio Schlock.
- Wiring errors of one type or another. I assume you're clear on the 7805 pinout. In the photo below, left to right, are Input, Ground, Output.
Not clear whether you've wired up the whole circuit (hope not because the MCU won't like 8V very well, could very possibly destroy it), but I'd suggest just building the power supply section until you can get it working properly.
