Can I use a 205 55r 16 instead of a 195 65r 15 on my 2010 Toyota Corolla ?

Not without changing wheels.

I think you will be fine. Now, with 195/55-15 your total diameter is 24.98" and going to 205/55-16 will be 24.88". --1/10 inch difference in diameter. And10mm wider. If there is the same amount of room in the wheelwell of your 2010 as there is in my 2006 it won't rub from being wider

Well yeah.....I could have remembered that DOH!

Let me clarify my answer. That tire size should work fine, but will require 16" wheels.

I should know better than try to answer a question at 5:30AM.

FordNut, you did fine.