My kids bathroom light keeps turning itself off after about 5 minutes. Then after 10 minutes or so it will turn itself on again, and so forth. I am wondering if this is something relatively simple that I can fix?
If the light is recessed, check the bulb size as to compare to what is rated for the can. The rating will be on a paper label glued inside the can. Too much wattage equals too much heat and the thermal unit inside the can is doing its job, turning off the lamp to cool down and turning the lamp back on when it is safe. It will repeat until the lamp is replace or the thermal unit goes bad, which means a costly or time consuming repair.
Of course, if it not a recessed light it probably what @Niall C. is talking about.
An intermittent problem like this could be caused by a combination of a loose connection and the waste heat from the bulb. As the bulb and light fixture heat up, they expand eventually causing the loose connection to be broken, turning off the light. With the light off, they cool down and shrink, remaking the connection so the light turns on again.
This could be dangerous as you could get arcing across the connection at the points where the light turns on or off, which can cause electrical fires.
To find and fix the problem: