How to reduce wheel gap with tyres/rims

[affifi]

Hi guys, I have no idea how rim and tyre codes work but I would like to make the wheel gap smaller. Which rim size and tyre size can I go to to make this happen. Supposedly I have 5Jx15 ET39 rims and 175/65R15 tyres (2017 Yaris Icon D-4D)

[local hero]

Try here https://tiresize.com/calculator/

[TonyHSD]

Another website that you can use to locate available wheels and tyre sizes for your car make and model. https://www.wheel-size.com
https://www.willtheyfit.com 
Reducing arch gap only does make no sense or difference, I don’t know why are you after this ? If you want to make the car look sportier you can perhaps buy larger wheels with low profile tyres to match the set and be within the car specs. These two websites will give you plenty of options to play with. 
Good luck 

[Strangely Brown]

You cannot make the gap between the wheel and the arch smaller without fitting a wheel/tyre combination that has a larger diameter and by extension a larger rolling radius thereby making the speedometer read under the actual speed and therefore be illegal.

You may be able to give the illusion of a smaller gap with larger wheels and lower profile tyres, which will likely ruin the ride and alter the handling, but if you want to actually reduce the gap then you will have to lower the car.

Sorry for the bad news, but I have a question...

Why?

[Mojo1010]

Above ask why? It's most likely to look better/sportier. 

If this is the option you want to take then get a set of 16" for the MK3 with 195/55/16. This will make the car handle a lot better than the 175mm, I had 175mm on the mk3 hybrid, its too small, handles very poorly even around slow corners. 

[bathtub tom]

You'll also need to inform your insurers of this non-standard modification and be robbed blind for the premium increase. If you don't inform them, they could welch on any claim. Do you think it's worth it?

[Derek.w]

If you after a smaller gap between top of wheel and wheel arch dont do it if you do your speedo  will need recalibration. You maybe able to find shorter springs to acheve the same look!.

I have no idea if a set exist for your car.

[YarisHybrid2016]

Another vote for "why"??

Just lower the suspension if it bothers you that much, but be aware that the "gap" is actually there to allow compression of the suspension.

I've seen cars with the wrong size wheels on spacers (so they stick out beyond the wheelarch) get destroyed because they hit the wheelarch going over a bump.

...not to mention many of these mods are illegal!