Shrinking seems to materially benefit humans a great deal there but, wait a minute... Natural disasters, some insects' bites and whatnot are bad enough for normal-sized humans. Now try to imagine with 5-inches tall humans... Also, who would want to go from the top of the food chain to the near bottom, with cats and dogs as giant monsters? Life would be barely better than Gulliver in Brobdingnag or Honey, I Shrunk the Kids for downsized people should whatever protection their communities have from the normal-sized world break down.
Shrinking per se would not solve the overpopulation problem. What would stop the miniature humans from repopulating the earth to a problematic degree in a couple generations?
Several real-world measures intended to save resources have a similar problem if left to follow their natural course. For an extremely simplified example, you want to reduce oil use, so you make new cars that can cover more ground with less fuel. Once the new cars become widespread, people use them more, and some people who were too poor to afford fuel before, now can, because less fuel is needed for the average commute. The end result is that less fuel is used per car and per mile, but cars collectively use up just as much fuel as before, if not more.
The resources used by five inch tall people would be so much less that it would certainly take more than a few generations for overpopulation to be at all an issue (even at full size it's only an issue in certain areas in the real world, as evidenced by how many people starve yet the world is able to produce more than enough food to feed everyone, it just isn't able to get to everyone). Also, richer societies tend to have a far lower reproductive rate (a number of first world nations maintain or grow their populations through immigration as they don't reproduce enough to do so), so if anything the miniaturized population would shrink over time. Overall the many dangers that could arise for people from being such a small size (including being at the mercy of full-sized people) would probably be more of an issue than overpopulation or overuse of resources.
The adults have a choice to be shrunk; their babies don't. If you grow up and decide that being 5 inches tall is a horrific existence... tough breaks, kid. It's one way.
Of course, this goes for most conditions babies are born into (not to mention just existing). Parents' decisions will shape much of their child's life, good or bad.