195/65R-15s are speced at about 840 revs per mile; 205/55R-16s are about 845, so you're within about one percent of OEM calibration.
It's best to do this calculation when you are evaluting a new tire size and select a size that is close in revs per mile to the OEM tires.
In this case you were lucky. Revs/mile for makes/models/size of tires are listed at The Tire Rack under "specs" when you are viewing a particular tire, and they are also listed on manufacturers' on-line catalogs.
Tire and Rim Association standards allow a total range of about 8 percent for most specs, but most commercially available tires are very close to nominal, so revs per miles specs vary little from one manufacturer to another for a given size.
Another thing you should consider is load capcity and not go lower than the OEM tire. This can be an issue with low profile tires because load capacity is roughly proportional to contained air volume, so a same diameter tire on a larger radius wheel will often have LESS load rating that OEM despite being wider. A quick index of the load rating is the two or there digit number following the size, which is followed by the wet traction and temperature rating. The maximum load at maximum cold pressure is also placarded on the sidewall in plain English and metric units, and is also included with manufacturers specs.
In the case of the two sizes in question the load capacity is the same or very close.