:) Can I shut off the city water when I have a gas hot water tank for 5 months while on vacation?

Yes, you MUST turn the hot water heater OFF or to PILOT. If it's turned OFF you will have to re-light the pilot if it has one when you get home.

Turn off the cold water to the house and open a hot water faucet somewhere and leave it open somewhat so, the water has a place to go while it's cooling. Leave it this way when you leave.

You might want to drain the cold and hot water lines as well.