175 width tyres

That tire would be WAY too small for a Prius, especially a GenIII. Not only would the diameter be too small by a whopping 2" the load rating is much too low for the weight of the Prius. You need an 88 load rating or higher except in the case of the low profile 215/45/17s which are 87 but compensate with more robust construction.

What does all that mean?

You'll suffer very sloppy handling, braking distance would increase, mpg would decrease, tire blowout is increased greatly, emergency handling suffers as would highway straight line stability. I.e. don't do it.

 

Plus, a 14" wheel, even if hub, offset and bolt pattern were correct, might not even clear the brake discs...

 

205/55/16 = Yes
205/55/15 = NO

I hope you're not doing this because you are trying to source cheap tires. Cheap non-LRR tires may cost you more in the long run vs. a good LRR tire.

 

Here is a good website for figuring out what kind of tire/wheel combo will work on the Prius. Just get the stock wheel & tire inputed into the left side and compare with whatever you want on the right side:

Custom rims, wheel tire packages for your ride - RIMSnTIRES.com

 

The lowest specification Prius L in Japan wears 185/65/R15, apparently on the same wheels as the 195/65/R15. Gets a few more km per l than the wider-tyred models.
If you reduced to 175 on 14", you would need something like 80-ratio if you could find them to maintain outside diameter.