You will not keep that cl level at 5 for long with no CYA. Check the cl at least morning and evening and afternoon if you can and add more bleach so your cl doesn't drop to zero. You'll have to dose it frequently with bleach until you get some CYA in there.
Are you going to continue to use the trichlor pucks? If so, here is what I would do. I would go ahead and buy some stabilizer and add enough to get the CYA reading to about 20. Then, you can use the pucks awhile and build the CYA up to about 50. After that, no more pucks and no dichlor shock either or your CYA will get too high.
The other option is to not use the pucks and just add some CYA separately and go ahead and add enough to get to about 40. We also shoot a little low. It is easier to add a little more later than it is to remove it when there is too much. Either option will work.
You can just use the tabs and not add any CYA but the only issue with that is that it will take some time to build the CYA up and until you have much in there, you'll have a hard time keeping chlorine in the pool especially on a hot, sunny day.
To add CYA you can either pour it slowly into the skimmer while the pump is running and then let your pump run 24/7 for at least 4 or 5 days to give it time to dissolve in the filter. Or you can put some in an old sock and hang that in front of a return jet and let it dissolve that way. You can squeeze the sock every now and then to help it dissolve faster.
Your pH is too high. Add a little muriatic acid in front of a return jet while the pump is running. Wait a couple of hours, retest pH, and redose as needed. (If you have a sock of CYA there, remove it before adding muriatic acid.) I'd start with a pint of acid. Wear gloves, glasses, stay upwind of fumes, pour close to the surface of the water so it doesn't splash any.
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