Do I need a hotshoe adapter to fire studio lights with my Nikon D5000?

Or is there already a plug for them in my camera. I want to fire two lights.

If the studio lights are on optical slaves, then you could set the built in flash to manual, set it to minimum power, and use a white paper or tinfoil to aim the light away from the scene you are photographing. (Leave space in front of the flash to allow heat to dissipate, otherwise you might damage the camera flash.

There are also radio flash controls, such as Pocket Wizard and Radio Popper. One unit would be on your hot shoe, the other(s) would be attached to your studio flash(es).

Look for a PC (flash) connection on the body of your camera (or hidden under a door on your camera).

But, I highly recommend against having wires coming out of the camera - it increases the change of damaging the camera.

I don't think your D5000 has a PC sync cord socket for studio lights, so you can either fire them optically (most studio lights have an optical slave) using your pop-up flash on manual at minimum power, or buy a hotshoe-to-PC adaptor. Better still get some radio triggers.

The RF602's are excellent triggers and they are available with an optional cord which attaches the receivers to studio lights. They cost around £25 for a set of one transmitter (which goes on the hotshoe of your camera) plus one receiver. This will trigger one studio light - to trigger the other, either have the optical slave trigger off the studio flash which is radio fired or get another receiver.

The Nikon AS-15 adapter will add a PC socket to your camera. You only need to connect to one of the flashes, the second should be set to fire from the optical slave.

But I think the basic radio triggers from Hong Kong will work just as well, and don't cost much more than the AS-15.