60 watts / hr X 5 hours = 300 watts.
It'll take your solar charger (pwm, and acceptable but not awesome) and panel about 2.5 hour of full sun to charge the battery. Your solar setup is okay.
I'd change the battery.
Your as described battery will probably last a year or two with that set up.
A small lead deepcycle at 100 amp hrs would be 1270 watts. You use 300, should last 3-5 years. Don't forget to water. And if you have an equalize setting on the controller use it. The battery will last longer.
A small lithium battery at 40-50 amp hrs would be 600 watts. You'd use 300 which is 50% dod. Hopefully last 10-15 years. Make sure you don't overcharge the battery. Pick a charge setting that charges only to 14.1 is best. No need to equalize/water.
Good luck.
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