Performance-wise, this is the usual problematic iMac 8 GB HDD configuration, though this is a 27” and the memory is at least easy to upgrade. And this (failing) hard disk is slightly faster than the usual slower model that some iMac configurations feature.
It’s also featuring a hard disk drive which is failing. Hard disks that are failing are replaced, not repaired.
Usual recommendation for these iMac configurations is adding and migrating to and booting from an external SSD, but this Mac is old enough to have slow external I/O (USB 2.0) and the performance of an SSD on that connection won’t fair all that well.
Which leaves swapping the (failing) internal HDD for an SSD, or retiring this (failing) ~11 year old iMac.
And as previous replies have mentioned, no backups effectively means that the data here has no value, or can be easily reconstituted or rebuilt from other sources. Particularly with failing main storage. Getting a backup here would be my first and highest priority, if the data on this (failing) iMac does have value.
Get a backup. Then decide if you want to spend money on a 2010. Or replace it with a newer (used, refurb) or new Mac.
ps: This isn’t Apple Support you’re discussing with. We’re other users, like you.