I'm not sure of the Nexus 5's theoretical max refresh rate (common sense would imply it's 60, considering it's a modern IPS display), but Youtube is always 30 fps. That's what the videos are recorded at. It can't be changed.
As far as games are concerned... Don't bother hoping for 60 fps in mobile games. Nobody puts that much time into optimizing them or budgeting system resources from scene to scene. The framerates aren't consistent enough in most mobile games to bother aiming for a specific number of frames per second.