Does the Arduino Yun have to be powered exactly at 5V?
It is fine. That is only 2% too high. The microcontroller is the ATmega32U4 and it can have 5.5V. The wifi module runs at 3.3V, and it has a voltage regulator. Some voltage is also lost in the cable. If the voltage is 6V, then you are in the danger zone, but not with 5.1V.

There are clones and shields of the Arduino Yún. Each has its own power supply demands. You should read what the specifications are for your board. The official Yún board requires 5V from the USB cable or 5V at the VIN pin.