Smart man! taking good care of your septic tank will save you lots of money.
If you are concerned you could leave your sanitizer bucket in the sun for a few days. Or pour the water into the toilet bowl to flush the toilet. That usually works just a well as pulling the handle on the tank if you have several gallons.
I agree with david. I don't think even 5 gal. of sanitizer is going to have much effect on the anaerobic bacterial. But it really depends on the load factor of other such disenfectants you are flushing down the drain, amount of water you are using, the amount of waste you are puttin in and the age of a tank. I would not put it into a brand new tank.
Counting my childhood home I've been on a septic tank for 43 years and neither I nor my folks have ever experience a digestion related problem. And although we take good care of the tank we have flushed lots of chlorine and other disenfectants down the drain. Also neither of us has ever used one of those digestion enzimes such as Rid X a huge waste of money IMHO.
A real killer is DrainO but ever that in small doses won't kill all the bacteria.