To my knowledge the 5300 battery uses fairly standard NiMH cells. AAs I believe - but don't quote me on that. They're a nightmare to crack open without damage, but the standard cells should make a rebuild fairly easy if you have the proper tools. (I don't). Even if you can source a new battery, they're usually overpriced and they often use poor quality cells. Rebuilding is a pain, but it might be the best solution here.
Also, there's a good chance that if you can find a "new" battery, it might be years old. It seems that the last time these batteries were commonly available was around 2015. I do believe NiMH batteries have a pretty long shelf life, but you may be buying a 5+ year old battery that just happened to be just lying around from when they were still produced.
One more thing:
A lot of these battery websites have a ton of bad reviews claiming DOA batteries, horrible customer service, and other issues. I couldn't find anything on this site specifically, but that's the problem. I couldn't find anything, no reviews. There's a good chance they're a great source for batteries, but I just have a hard time trusting any of these battery sites. They all seem to just sell the same cheap stuff that doesn't last very long before dying. It's a real shame it's so hard to find high quality replacement batteries.