iMac will not recognize external USB DVD drive

iMac 21.5" late 2013 running Mac OS Mojave 10.14.5. 2.9 ghz Intel Core i5, 8gb ram, 1 TB SATA drive with 892.42 gb free. The iMac will not recognize a generic brand external DVD drive. Purchased an Apple brand drive with the same result. Apple support had us re-install OS, still no good. Their next suggestion was to wipe the hard drive and then re-install OS. Spent 2 hours on phone with Apple support. Checked drivers, etc. There has got to be a better solution than wipe the hard drive and re-install OS. What do you think? I don't have much experience with Mac, mostly with PC, but willing to learn.