No—on the Nikon D5000, the live view timeout is generally not something you can fully disable. It is there to protect the camera, mainly to reduce sensor heat buildup and heavy battery drain while Live View is active.

That means the camera will shut Live View off automatically after a short period, and for this model it’s a normal limitation rather than a hidden option you missed. One community reply mentioned a timing setting on a different Nikon model, but for the D5000 the consensus is that this behavior is intentional.

For video or long Live View sessions, the practical answer is to work within that limit or use a camera designed for longer video/live-view operation.