15" ??? What year car is this ??? use the "User CP", up in the blue bar ^^^ to put your car, year, mileage in your login header.
Go to www.tirerack.com and look up the specs on a good all-season tire for your car's original tire size - on the driver's door sticker ? Then look up the specs for the new tire. If the outside diameter of the two tires is within 0.3 inch or so there will be minimal effect on speedometer or handling performance.
The 205 is still in the ball park for diameter. 70 verses 75 aspect ratio (width) not a huge difference there either but if you are buying new get the proper size for the rim width. The side wall will then be correct and the bead won't be pinched in by too small a rim width assuring expected tire performance.
Is there any downside if I use a 205/70-15 tire in lieu of the specified 205/75-15 size?
The 70 or 75 in the tire size stands for the approximate percentage of sidewall versus the tread width. A 205/75-15 has a sidewall height of 205x.75=153.75. A 205/70-15 has a sidewall height of 205x.70=143.5. When you go down in sidewall heigth you have to go wider in tread width to keep the same approximate tire heigth. If you go to a 70 series tire you can go up to a 215/70-15, 215x.70=150.5. This tire will be slightly smaller in diameter but the extra 10mm in tread width should not be a problem.