You can but shouldn't. If you chose to do so, you would decrease the circumference of the wheel and therefore your top speed will be lower, but acceleration a bit higher. Your speedo will also read wrongly, but not by much, and it will overstate the speed.
The real answer to this question comes from an understanding of what all the numbers mean. The 225 is the width of the tyre in mm. The 60 and 65 are the profile of the tyre, or the ratio of height / width. So, the height of the 60 tyre is 60% of the width, and the height of the 65 tyre is 65% of the width. The R means that its a steel radial tyre. The 17 means that it fits a 17 inch rim.
The overall diameter of the 225/60R17 wheel and tyre combination will be 17 inches (431.8mm) plus 2 times 225 * 0.60 = 431.8 + 270 = 701.8 mm
The overall diameter of the 225/65/R17 wheel and tyre combination will be 17 inches (431.8mm) plus 2 times 225 * 0.65 = 431.8 + 292.5 = 724.3 mm
So, the answer in the first paragraph is correct. The explanation above is why. Only one more thing to add to the first paragraph. Using the 60 tyres instead of the 65 tyres will give you better braking performance. Or, in other Words, your brakes will not have to work as hard to stop the vehicle, but you might be more likely to lock up the brakes, and skid. This is because the 'lever' length is shortened. i.e. The distance from the centre of the wheel to the road surface is reduced, by 22.5mm, so it easier for the brakes to stop the vehicle. This isn't a major problem, because you should get used to it relatively quickly.
If you fit the 60 tyres instead of the 65 tyres, you will be travelling slower than your speedo indicates you are.
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