Pilot light will not stay on after holding down for over 5 minutes... can this be repaired without replacing the tank??

Hi! You just need a new thermocouple. Depending on where you purchase it $9-$20.

It is furnace oriented, but more on thermocouples at https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html

You do not need to replace the tank. If you need more help please feel free to ask. Being new to this site the other experts feel someone else may be more qualified to answer you question. I am happy to step down.