Spokes break at four main points
- at the J bend becuase they've been ridden too loose, undertensioned
- In the rear wheel, about 10mm along from the J bend because the chain has jumped the big cog and munched the spokes. Normally the outboard ones take the damage.
- At the spoke nipple because of excess tension and age/fatigue. The thread can be a stress riser, sometimes exacerbated by a smaller rim where the spoke has to turn shaper
- Mid-span - this can be any combination of fatigue from old age, along with damage over the life of the bike, or perhaps a manufacturing flaw that finally broke.
For an older bike, especially one with an unknown history, its possible the bike was in an accident or fall and this has put a nick in the spoke.
Rust can also build up over time. This is delayed by having chromed spokes, or anodised on newer bikes, or galvanised on older bikes.
That five spokes have all gone implies they're not independent events, and something caused damage to them all. Or the whole wheel is made from cheese.
If it were my wheel, I'd give it a clean, then a close inspection. Take it out of the bike, remove tyre/tube and clean it well, right between each spoke.
Tap each spoke in turn around the wheel, both sides. Use something metal like a screwdriver. You should hear "similar" tink-tink-tink sounds, with none of them sounding super high or low. That would imply high or low spoke tension.
I'd also give each crossing pair of spokes a good hard squeeze so the crossing slides. Perhaps wear gloves in case one breaks in your hand.
The result of your inspection should be a decision to replace the broken spokes OR all the spokes, OR to replace the whole wheel.
I've had good luck checking local auction websites with patience, rather than buying brand-new wheels.
Ultimately, you should learn to replace your own spokes. Each one costs a couple of dollars, but the bike shop will charge 10x that for labour.
The only special tools you need are a spoke nipple wrench that snugly fits your size of nipples, and on the rear wheel you may have to remove the cassette/freewheel to get access to fit in a new spoke. And you'll need the spoke itself (and a nipple if the old one gets lost). Some people use a "spoke prep" lube on the threads that thickens up after assembly, but that's optional.