n4zou: "...Rear derailleurs come in two ratios, 1:1, which covers everything up to 8 cogs and 2:1 ratio for 9 and 10 speeds. With the introduction of the 9 speed cassettes 2:1 derailleurs had to be used due to the very close spacing of the cogs..."

--- SRAM's current "ESP" 7, 8, & 9-spd derailleur/shifter systems are 1:1 specific. ~ They will not shift well with Shimano units. ~ Their cassettes are compatible. ~ The ratios used has nothing to do with the spacings of 9 and 10-spd cogs.

"...The space between the cogs is the same for 5 and 6 speeds and then changes for each of the 7, 8, and 9/10 speed freewheels/cassettes... Pretty much any index shifter for the number of cogs on the freewheel or cassette that matches the number of indexed shifter will function fine...."

--- It is impossible to get a 7, 8, 9, or 10 speed Campagnolo shifter to shift correctly on a Shimano 7, 8, 9, or 10 spd cassette, and vice-versa. The cogs on their cassettes are spaced differently.
--- And, each of their 9 speed cassettes are also spaced differently than on their own 10 speed cassettes.

Sorry, about the digression, this is all totally off the track...

--- @¿@ --- I think that the fastest, easiest, cheapest way to get the bike back on the road would be to:
1.) Go to a Local Bike Shop and spend around $15-25 on perhaps a Shimano "Tourney" rear derailleur (which are solid workhorses, good for up to 7-speeds), or another basic traditional "top-normal" (not "rapid-rise") derailleur.
2.) A good time to replace the derailleur cable(s) and replace the rear cable housing with a modern "compressionless" (SIS-style) loop [all for just a few bucks anyway].
3.) Buy a new chain [$10-$15] (since the old one has probably stretched greatly during the past 25-30 years, anyway or was possibly damaged when the derailleur jammed). A worn chain will tend to slip gears on your freewheel.

Perhaps even consider a new freewheel [for maybe $20] - Shimano, Falcon and Sunrace all still make 5-spd, 14-28 tooth freewheels. They all work. But, Don't let the shop try to squeeze on a standard 6-speed freewheel just because they happen to have one. It will stick out too far over your axle.

If you still want to get indexed,... Shimano ALSO still makes CHEAP and INDEXED "Tourney" handlebar mounted thumb shifters [model TY-22 or TY-15] which you can clamp onto the tops of your handlebars... last time I ordered some (2005) they were under $15 for a pair. But, I suspect your LBS would no doubt have to order a set, since they really cater to newer components and replacements for more modern broken toys. You can always add something like these later.

Remember, if you do want MORE than 5-speeds, you will need a new (longer) rear axle... AND,... you will have to re-dish your wheel... AND,... you will then also need to re-space and align the rear of your frame from 120mm to at least 126mm. Your LBS will charge you insanely for any/all of this.

Dad's derailleur "exploded" on you because the chain jammed somewhere back there. Make sure any replacement has its limit screws adjusted properly. If so, the chain really shouldn't ever get thrown.

Also, have someone check the rear derailleur hanger and dropouts to be sure everything is straight so everything shifts smoothly together. If a derailleur hanger is not straight (parallel with the frame), you'll always have problems with shifting or a chain slipping gears. If the dropouts are not parallel to each other you can also have problems with your hub bearings and axle. These are very fast and very easy adjustments to make on a steel frame, but they can make a big difference. They both require simple but specific shop tools.

And, lastly, just make sure there are no excessively long bolts or nuts from a poorly mounted rear rack or fender getting in the way of the chain when it is shifting onto or off of the smallest cog. - Yes, I've seen someone jam up a brand new drive train because they had put on a rack and the chain got snagged by a long bolt poking just above the freewheel.

Good Luck. Those were very nice bikes. You should have little difficulty (or expense) getting everything spinning very smoothly once again.