You might be disappointed even if you could find a 5.25" drive. About ten years ago, my cousin and I got out the Commodore 64, a 1541, and a stack of games. About a quarter of the games were no longer readable by the disk drive–and we tried several disk drives (my cousin kinda collected these things). Of course, they were all pirated games copied onto store-bought Maxell disks, but I’m not sure the manufacturer’s disks are necessarily much better.
What’s important with a CD isn’t the physical medium it’s encoded on but the tasty data it contains.
If you have audio CDs you want to back up with assurance, I suggest Exact Audio Copy – this program will rip the data from an audio CD with extremely high precision. If your CD is damaged it will tell you exactly where and how damaged it is.
Burning this data onto a new CDR you can be sure that you have a good and solid copy that will last. Better, you can keep the digital data electronically. Heck, I keep most of my audio CDs compressed (lossless) with Monkey’s Audio on my HD with a few physical backups just because I hate the thought of losing an old CD.
I’ve got one here, in the bay underneath my DVD burner. 
I just put it in there to be anachronistic, but it works fine. I can transfer that game to something more modern if you’d like, although you’d certainly need Dosbox or something to run it.
PM me if you’re interested.
The CD audio standard Compact Disc Digital Audio - Wikipedia defines what the data on the disk has to look like. It doesn’t define how the player has to work.
So a cheap player could choose to eject the disk as unplayable the first time a raw bit error came off the read head. Meanwhile, a better player, or an app dedicated to data recovery, could apply the ECC to regenerate the damaged bits & there would be zero detectable difference in the bit stream leaving the ECC stage & heading into the digital-to-analog (DAC) converter stage which eventually comes out as music.
So a general answer to your question does not exist. Different players will handle the same disk with the same errors differently.
As a general matter, the ECC was designed to deal with physical scratches. So the data is interleaved in such a way that a few dozen bits in a row being unreadable isn’t a problem; the rest of the logically nearby bits are physically far enough away that they probably aren’t under the scratch & can be read reliably; if so the ECC can put it all back together. This is the reason for the instruction to always clean CDs by wiping radially, not circularly. If you scratch it, a circular scratch may obliterate a long-enough run of data to be uncorrectable, while a radial scratch (unless implausibly wide) won’t.
A rough hierarchy of error correction responses from least to most audible:
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ECC-Correctable single- or multi-bit error: No change in bit flow into DAC, so no theoretically or practically detectable change in audio output.
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Single ECC-non correctable error: The ECC module knows this particular signal sample is bad, and can’t figure out what it ought to look like, so it interpolates between the previous & next sample which are known to be good. Then it outputs the interpolated value instead of the damaged one.
Since samples are taken at 44.1KHz, that’s very roughly 20 microseconds of missing audio. The audible effect of interpolating between two samples 40 microseconds apart would only be detectable in principle if there was an attack & decay shorter than 40 microseconds. As a practical matter human ears couldn’t detect that and so human music doesn’t contain such signals.
- Multiple ECC-non correctable errors: The ECC module knows it can’t tell what several sequential signal samples ought to look like, so it interpolates between the last & next readable ones. These repairs are obvious to a signal analyzer, but may not be audible. There are also tricks where you can use valid left channel data to substitute for defective right channel data & vice versa.
For maybe up to a few milliseconds, say 400 consecutive samples, whether the interpolation correction is audible or not depends on the music. If the fault occurs right in the middle of an agressive attack, say a drum hit, you’ll hear that it “just ain’t right”, if you’re paying close attention. If it’s in the middle of silence, or a sustained violin note, you may not be able to notice anything no matter how hard you try.
- Excessive ECC-non correctable bit errors, sync not lost: Beyond a built-in threshold, the ECC system chooses to output zeros rather than interpolate. It’ll begin output again once it receives valid data from the read head. When the zeros hit the DAC the result is audio output is muted. This is almost always audible and sounds like a skip.
The threshold between behavior 3 & 4 is one of the big areas of ECC quality difference in players. It costs money to add the memory & processing power to play through longer errors. This was especially true in the earlier (1980s) players when there weren’t cheap single-package ICs for doing all the processing. This is also where portable players need more ECC since they’re prone to long (fractions of a second) data dropouts when the player gets jostled.
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Sync lost. The ECC loses track of where it is on the disk. The ECC output goes to zeros until the player can recover where it is. Every so often mixed in with the audio are “signpost” data & it just scans ahead until it finds a signpost. Small examples of this produce 1/2 to 2 second gaps in the audio. Larger examples do different things with different players. Some players will automatically try a “fast forward” for a few seconds-worth of audio & regain sync in the track, others will just get “stuck” and won’t play the rest of the track. For the latter case, manaully fast forwarding may recover sync, maybe not. In most cases you can manually track advance to the next track & the player will sucessfully locate the next track & resume playing.
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Disk unplayable: Things can get so screwed up the player can’t find enough usable signposts or the disk’s table of contents is trashed. The disk just doesn’t play.
Armed with all that, whether an old CD will play depends a lot on how it deteriorates.
If isolated single bits just go stupid entirely at random, the disk can probably lose 10% of the bits before you notice any audbile degradation. By 15% there are a bunch of gaps in most tracks, and at 20% it won’t play in most players.
OTOH, if rather than single bits failing we have blots, say, 3mm in diameter that go bad, and these are scattered randomly over the surface, you’re going to start getting audible gaps at more like 5% coverage.
A single dead spot 1" in diameter will make all tracks touching the blot unreadable. Whether you can get to the undamaged tracks on the far side of the blot depends on the player; so will, some won’t.
If the disk deteriorates by the surface flaking off, then you can expect failure to play as well as permanent damage to the player.
I don’t know enough about CD deterioration models to offer a prediction. I also expect that factory CDs will have different failure behaviors from home-made CD-Rs, which will have different failure behaviors from CD-RWs. There have also been improvements in manufactruring for all 3 kinds od CDs over the years, so I’d expect the earliest examples of each type to have poorer longevity than later examples.
In general I’d suggest that in this case ECC is not your friend in the sense that it will mask many forms of deterioration until the deterioration is very close to critical. By the time you can hear overt problems, you’ve got a very sick disk on your hands.
Gamehat’s Exact Audio Copy would be good tool if you’re really interested in health monitoring of archival CDs.
p.s. Sorry for the dissertation; I got on a roll.