Getting 3.3v on 5v pin in Arduino Uno
and an external 5V DC power supply


OK, assuming you are putting 5V into the barrel jack this is exactly what you expect to happen.

From the Arduino Uno specifications you are supposed to supply a recommended 7V to 12V. Your supply of 5V is too low.

The barrel jack first goes through a M7 protection diode which would have about a 0.7V forward voltage drop, and then through a NCP1117ST50T3G voltage regulator which has a dropout voltage of (typically) 0.95V at 100 mA.

Thus you have:

5V input - 0.7V - 0.95V = 3.35V


That is what you are finding.



Solutions


If you have a proper, regulated, 5V DC supply you can put that directly onto the 5V pin of the Arduino. Better get the wires around the right way because you are bypassing the protection diode!
Get a DC supply in the range 7V to 12V and put that into the barrel jack.
Another simple idea is to just get a wall-wart that is used for charging phones via USB and run a USB cable into the Arduino USB port.




Empirical test

I put 5V into the barrel jack of my Uno and read 3.33V on the 5V pin, which is pretty-much what you got. I measured a 0.77V drop over the M7 diode.