Instead of welding, it would need to be brazed. If were you, I would check with the guy above Roy Underhill's shop and see if he could recommend someone. Bill Anderson could also be another lead.
Probably type 11 or 12. I have a a type 10 No.5 base. Close, but no cigar.
You can probably find a replacement base on eBay, but as Mike stated, you may be better off just looking for a another No.5 that you can refurb.
As much as we hate to lose a good well-designed tool, there comes a time when they meet their demise. Luckily, decent #5s are not that hard to come by.