www.1010tires.com has a calculator to determine this.
I ran it for you, they warn that you should not exceed a 3% diameter change from stock, or risk braking problems. In this case, you are just over at 3.18% . Also, note the speedo error.
The key here is that the 65s are larger diameter than the 60s. If they are worn a bit, you would actually be under 3%. Ehh, I'd probably put 'em on if they are free... it's close enough....
Stock Tire - 205/60R15 >Search Tires Tire 1 - 205/65R15 >Search Tires
Section Width: 8.07 in 205 mm
Section Width: 8.07 in 205 mm
Rim Diameter: 15 in 381 mm
Rim Diameter: 15 in 381 mm
Rim Width Range: 5.5 - 8 in
Rim Width Range: 5.5 - 7.5 in
Overall Diameter: 24.68 in 626.87 mm
Overall Diameter: 25.49 in 647.44 mm
Sidewall Height: 4.84 in 122.93 mm
Sidewall Height: 5.24 in 133.09 mm
Radius: 12.34 in 313.43 mm
Radius: 12.74 in 323.59 mm
Circumference: 77.53 in 1969.2 mm
Circumference: 80.07 in 2033.7 mm
Revs per Mile: 842.7
Revs per Mile: 816.0
Actual Speed: 60 mph 100 km/h
Speedometer1: 58.0 mph 96.8 km/h
Speedometer Difference: - Speedometer Difference: 3.272% too slow
Diameter Difference: - Diameter Difference: 3.18%