That depends on the current technology. I still have some very old Sony BetaCam tapes, you know the ones that were battling with VHS. While they are not in like new state, having fall-off, the video is still watchable. Those tapes would be about 25yrs old now, and tape media was considered to be very fragile.
We really don't know what the life expectancy is for DVD or Disc media. There's so many variables at play to provide a single definite answer. Pressed discs will probably have a longer life than burned discs. Discs are burned at different speeds, the slower ones may last longer if the theory is correct that the data is burned into the disc deeper. Not sure about that though, as I had one disc that I made about 8 yrs ago, and it no longer will play on anything. The burner I used back then could only burn at 4x, which is considered about the slowest speed now. You also have to look at the quality of burner used, and quality of blank discs. Then to top it all off, how well they are stored.
I guess when we know a definite time, we can let you know. If they last as long or longer than my old Beta tape, I'm not sure I'll still be around to tell you though..

It also may be that the disc out lives the devices used to play them, in which case how would we really know. Solid State devices like Smart Cards, and even Solid State Drives are probably the most durable, since there are no moving parts. However those too are subject to failure. I have a 2-Gig SD card that I don't use any longer as it may work in my PC, but not the camera that it is intended to work in.