Can I get my Promaster 7500edf to flash when not attached to my Nikon d5000?

Do I need a flash trigger or is there some kind of setting for it to work?

When you purchased your flash, did you buy one made specifically for your Nikon?

That flash comes with hot shoe interfaces for Nikon, Canon, Pentax, Samsung, Sony and Olympus cameras. For that flash to work with the features on each of those cameras, the hot shoe connection must match (Sony has a proprietary mount) the connections on the host hot shoe.

You will need a trigger and a transmitter. Buy them as a set. Bring your camera and flash to make sure they are compatible with each other.