iMac won't read DVD-R and DVD+R

I have a couple of TDK DVD-R and Maxell DVD+R that I have used to store photographs on. The DVDs are about 12 to 13 years old, but I have tried reading a few on a Windows PC and so far all could be read without error. When I insert one of the DVD-R into my 2010 iMac running macOS 10.13.6, the computer futilely attempts to read the DVD only to eject it after a while. This is the same for all DVD-Rs. When I insert one of the DVD+R, my iMac tells me that I have inserted an empty medium and asks me whether I want to burn data on it. This is the same for all DVD+R. The iMac does have trouble reading newer audio and video DVDs, but it faithfully reads all my old audio DVDs. I therefore think that there is nothing wrong with the drive, like dirt on the lense, but a compatibility problem with the software trying to read the DVDs. What can I do?