Powering several amplifiers with one power supply
Yes, you can use a common power supply for all five amplifiers. The supply must be capable of providing enough current for the peak demand of all five amplifiers at once (e.g., 5 &times; 125 mA = 625 mA). For example, the NT101A/NT102A power supply shown in the datasheet has a rating of 650 mA, which would be plenty.

And yes, it does not need to be a regulated supply, as long as it always produces a voltage in the specified range.