Well water sanitizing and ph balancing questions
Clorinated organic compounds.  Some are carcinogens.  Some are nerve toxins.  That said, a well run chlorinator thatfilters the water first for organic matter then puts a 1-2 ppm residual chlorine level in the water is not very toxic.  Cities have done this for a very longtime.

UV treatment works too, and is the route I would go.

a pH of 5.6 isn't very acidic.  Remember that pH is a log scale. This is a level typical of eastern hardwood forests.

But I would get a full water analysis done.  Here (Alberta) we can get a sample bottle at our local public health office.  The analysis is free.

Take that and find out what needs to be done.