You should replace them ASAP.

There is no safe distance to drive on tires that show dry rot. They could blow out at any time as they are no longer structurally sound.

just long enough to kill yourself!

Once they start to dry rot it's too late, they're unsafe. Typically about 6 or 7 years is about all you can expect to get out of a set of tires before this happens.

Back in the "good old days" of bias-ply tires that would only last 10K-20K miles dry rot wasn't much of a problem because for most people the tread would wear out before rot set in. Today with tires lasting 40K-60K miles if you have a car that isn't driven much the tires can easily start rotting way before they're worn out.

I have several older vehicles that get driven very little. The tires on them typically need to be replaced while the tread on them still looks practically brand new. It seems a shame to toss out tires with good tread but that's just the way it is.

If you’re lucky, tread will separate a little bit from the dry rot and just go flat while you’re parked. You’ll come out to a flat tire that can’t be filled with air or plugged. If you’re not so lucky, it will happen while you’re on the interstate at high speeds and cause you to lose control of your vehicle. Do you feel lucky?