I have replaced the thermalcoupler and the pilot light and water heater stayed lit for about five minutes, and then all went out. I try to start it again and now the pilot light will not stay lit again.

What kind of water heater do you have ? Is it newer model, less than 5 years old ?

In the interim, please check this:

1. Vent is unobstructed
2. Gas line is not kinked and gas valve is fully open
3. There is "breathing" space around the heater

Back to you. Milo