265/70R17 is 1.61" taller than 275/60R17, a +5.38% change in diameter. That is more than the 3% many tire shops use as a limit, so plan on recalibrating the speedometer and checking ABS and stability control.
Ground clearance changes by 0.81" (half the diameter change), and the tire needs 0.81" more room above it.
275/60R17 is 0.39" wider. On the same wheel offset about half of that, 0.20", moves toward the suspension and half toward the fender.
Both fit a 17" wheel; the sidewall is 0.81" taller on 265/70R17.
Details: 275/60R17 in inches · 265/70R17 in inches · change sizes in the calculator