Question: I have an ISP that provides 5000 GB for use between 1am and 7am. Is it possible to schedule Geth to sync only during that time?

Answer: 
If you have a firewall that you can run that is time-based, you can simply block network connections for `geth` outside of that window. `geth` will pick up where it left off.
Syncing can not be restricted directly in the Geth software.

Some of the other answers give suggestions of possibilities - cron jobs etc.

That said, the Ethereum blockchain is not that big (< 30GB), and it syncs really quickly with the various fast sync [command line options](https://github.com/ethereum/go-ethereum/wiki/Command-Line-Options).

Just sync the chain manually between 1am and 7am. Keeping the head of the chain synced after that point will not use up much daily bandwidth at all.