Connecting a positive voltage to an Arduino OUTPUT pin
As the answer you linked to clearly states, PS_ON is an input. You can drive it with a 0-5V output pin just like any other 5V TTL input.

I think your confusion lies with the "5.25V" specification. This simply states that if the pin is completely open circuit (no current flowing), it can float up to as much as 5.25V. 

If you drive the pin with a 5V I/O line, it will no longer be floating. In fact it will now simply sink a small amount of current (μA's worth) into the I/O pin which will pull that voltage down to match the I/O pin voltage. This is not going to cause any problems - if you think about it, the amount of current flowing from the PS_ON pin will be much less when you drive it to 5V than driving it to 0V.