Depending on your intent, the cost of a project is either something that has a budget, or it doesn't. I have tons of tanks in the fish room, and each project that goes in that room has to have a real and tangible "end game". I have a planted hex in the corner of the den and a planted 180G peninsula in there also, that just have to look good all the time.
The others here have already commented that it would be a siginificant savings in time and $ to just buy a stock 5G at a LFS. In a nutshell, from a pure $ perspective, they are absolutely correct. A 10oz tube of silicone and caulking gun will approach the cost of a tank by themselves. The glass panels are a whole 'nother creature to tackle if you haven't worked with glass before. So the money side of it is something you really have to decide for yourself.
I haven't seen one of these tanks since I was a little boy. So what I say next, may or may not be correct. The stainless frame is formed to fit around the glass and slate members. In other words it was never built to facilitate replacing a broken panel. Even replacing the slate bottom would be a tricky deal. You can't just bend one of the supports and try to bend it back in place without a bunch of creases and tool marks. And then there's the sealant itself. It's thick "gooey" stuff. So that the glass dimensions change when you switch to silicone. Lastly: getting it off of the inside of the metal frame would be something even I wouldn't want to tackle, regardless of the potential of the end product.
I'm not necessarily trying to talk you out of it, but at some point, we all need to be realistic. If you're looking for a more nostalgic home for your betta, I think you can find other choices that will prove less frustrating in the long run.
Honestly, if you already have a caulking gun, a glass cutter, and some scrap glass, you would probably be better served by DIY'ng a small tank from scratch.