If the sentimental value of having the matching bbl is strong enough, then you could go ahead and have the work done as described above. Pricey, sure. Still not a shooter. But it's restored and that's what some people want.
Another way to have the the original matching # bbl,,or at least the look of it and still be a shooter is to use the orig bbl as a sleeve. You use another bbl with an excellent bore and forcing cone as the bbl itself.
Not relining,,sleeving takes the old bbl and cut's it off at the face of the frame, bores it out quite large straight through.
The other bbl, preferably a S&W bbl so you have the same factory rifling specs is fitted to the frame. This new bbl is fitted up for cyl gap, ect. Then it is removed and the entire length is turned down expect for a small shoulder at the frame abutment so the old bbl (now a sleeve) will slide over and onto it.
The sleeve bbl is given a small recess at the breech end to accept the shoulder cut on the 'new' bbl. The The sleeve is then permanetly attached to the new bbl. Solder used to be the way,,then epoxy,,now various Loc-Tite compounds are used with great success. Same as the liner attachment business has gone.
A close fit between the two and a slightly coned muzzle will make all appearances of the work dissappear if done carefully.
The 'new' bbl takes all the stress of fireing. The sleeve made of the old bbl is there for looks and carrys the original markings,ser# and 'look' of the family prized gun.
Not cheap either,,restoration rarely is but it makes the gun a shooter.
If you don't care about all that,,then just hunt down a 5" tube have it installed.