yes should leave on 24/7 for best results
Broadband routers and modems, including the Homehub 5 are designed to be left on 24/7 but it shouldn't make a lot of difference to your speeds if you do switch it off and on once a day. If you are thinking of doing this to save electricity I think the HH5 costs less than £10 per year to run so you won't save much. If you are doing it as a security measure, the HH5 has a built in fire wall and security which will prevent any attacks on your system.
The homehub generally gets updates during the night, which if you have it turned off, obviously won't happen.