RT-AC5300 is end of life so no new firmware to fix any bugs. Moving away is a good path if one can afford.
If you have AX clients, for sure you'll benefit from the bump in the protocol. Browsing speed will benefit by the increase in speed for AX clients, but not like you'd measure any improvement unless you're using very large pages and you really want to find that improvement (normal web browsing doesn't require really large transfers). AC clients will see no difference.
Latency has little to do with the router, unless it's a really underpowered (like really old) device.
I moved a couple of years ago from a GT-AC5300 to a GT-AXE16000. For normal daily use - no difference! Massive difference for AX clients and 6GHz clients for file transfer speeds. Especially after connecting NAS on 10G. But that's something that's useful when I transfer photos. Like one hours in some weeks, not weekly. I switched for 10G port and for nearly end of life (at that time).