Powering stm32f3discovery board from pin/external power
The white dots tell you where pin 1 is on the connector. You can also see that the solder pad is rectangular and not circular - which indicates the same on copper level.
If you have a look at the schematic you see the board uses a LD3985M33R to generate the 3.3 V out of the 5 V. The datasheet of that part indicates that it is able to run up to 6 V. It will be able to generate the 3.3 V down to an input of 3.4 V.
So from that I'd say 5.2 V is not inherently the problem. Depending on what the UBEC (whatever it is) does it can still damage the board.
The discovery boards do not include protection devices of any sort - so a voltage spike beyond 6 V could damage the whole thing. As will static discharge of your cat or a lot of other things which can go wrong. These boards are nice to evaluate the chips and build small projects which are not required to be rock solid. If you made the experience, that the MCU is able to do what you need and you need it 24/7 it's time to move on and make your own robust design.