Without a clear continuity to hang it on why should I care about what happens to me in five minutes, much less five years?
You care because your brain was created by evolution, which relies on physical continuity of your body. Whether you "should" care depends on your meaning of "should".
This will be a short article. I've been seeing a lot of dubious reasoning about consciousness and sleep. One famous problem is the problem of personal identity with a destructive teleporter. In this problem, we imagine that you are cloned perfectly in an alternate location and then your body is destroyed. The question asked is whether this clone is the same person as you.
One really bad argument that I've seen around this is the notion that the fact that we sleep every night means that we experience this teleporter every day.
The reason why this is a very bad argument is that it equivocates with two different meanings of consciousness: