Would this lathe have enough room between centers to do barrel work?

Yep Including 40" barrels. Give or take.

My 10L has a 4' bed and has 30" between centers
So I'd say a 13" should have about 36" between centers minimum

But I don't do barrel work between centers

How old is the machine??

It was made in 1967. I am a novice and have only had a year of classes at the local community college. I was only concerned if I ever wanted to re-contour (i.e. re-taper barrels).

67 is actually quit new relatively speaking. It could be in good condition.

Either way it should have the range to cut a taper.
Does it have the factory tapper attachment?? If it does you scored big those tapper attachments are worth their weight in gold it seems

Those southbends are nice. Some of my guys found one in a shop we have in san francisco being used as a coat rack.

My regional boss had it sent up to us in AK. I'm rusty on it but been practicing on regular stock with my threading. I havent even gone through all the attachments that it came with.

Of course it will be for work purposes only

That would be a perfect lathe for contouring barrels. My friend does them on a 13" 7 ft model. Most of those big South Bends didn't get used for everyday stuff; they are usually very true and in very good condition.

The seven foot bed on my 1947 S-B has about 47 inches between centers and my toy heavy ten with three foot bed has about 17 inches. S-B measures the whole bed length, including the machined headstock mount. Five foot ought to give you about 36-38 inches between centers. Plenty of space. I have owned a couple dozen of these lathes and they are good sound machines. I do have a scanned copy of the 1967 S-B catalog if you are interested I can e-mail it too you. Earl.

The biggest issue with these old, big, South Bends are if it needs some attachments. You can get the lathes very cheap, many times less than a $1,000.00, but a steady rest, taper attachment or 3 or 4 jaw chuck won't be cheap if you need one!

Well actually there is a guy on ebay that sells steady rests for these machines. All are priced at about $150 He also has chucks and threaded back plates.

Ebay is a wealth of parts it just comes down to how much do you want to pay.

The thing is you bought a Machine tool and it can make you some money or be a real convenience. Either way it is not cheep to tool up one of these. But Good used tooling is around and Good import tools are available too. Don't discount the chinese stuff it's the same as American tool You get what you pay for. there is american junk just as there is chinese junk. So do some research and get what you can afford.

I was looking at converting my old 1927 SB 9" Jr I could get a gear box for it and drill the bed and it would work perfectly. Proble was the Gear box was as much as I paid for the lathe.

So I waited for a deal and was prepared to jump. Then a 10L with a 4' bed showed up on ebay with no bidders The asking price was way to much $2500. But I emailed him he replied and we worked out a deal $650. Because he had no idea what it was or what it was worth and couldn't answer questions to people on ebay was the reason it didn't sell. So I made a low ball offer and he took it.
Machine was fully tooled and ready to run just plug it in.

Tools for cheep
http://www.tools4cheap.net/products.php?cat=7