I think not. What you're missing is the implied presumption that (a) the clock was once set and (b) at that time it was correct.
Therefore, in order for it to *now* be five minutes ahead, it *must* be running at fast by (5m/dT) seconds per second, and the reasonable expectation is that it will continue to do so.
Noboody (that I know of) thinks a clock that's 5m ahead will stay 5m ahead forever. It might take more than next week, but one can only expect it to keep gaining.
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Therefore, in order for it to *now* be five minutes ahead, it *must* be running at fast by (5m/dT) seconds per second, and the reasonable expectation is that it will continue to do so.
Noboody (that I know of) thinks a clock that's 5m ahead will stay 5m ahead forever. It might take more than next week, but one can only expect it to keep gaining.