2008 Chevy Malibu tire size

The question is rather "should you" rather than "could you". Can you put 205/70-R15 instead of 205/65-R15? The answer is yes, you can. The wheel can take it. It is the same width tire, except the sidewall will be 143mm instead of 133mm.

But should you do it? Then the answer will be no, you should not. Increasing the sidewall will make the tire "larger" and longer distance to complete a revolution, which your wheel sensor will show slower speed on the speedometer than you are actually driving. Your suspension is also designed to work best with 65-series sidewall, increasing the height may also have an adverse effect on how the vehicle will handle.