You have two circles, one with radius $r$ and the other with radius $R$. You wish for the difference in the areas of these two circles to be less than or equal to 5$\pi$. If $r+R=10$, what is the maximum difference in the lengths of the radii?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
You have two circles, one with radius $r$ and the other with radius $R$. You wish for the difference in the areas of these two circles to be less than or equal to 5$\pi$. If $r+R=10$, what is the maximum difference in the lengths of the radii?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{2}
You have two circles, one with radius $r$ and the other with radius $R$. You wish for the difference in the areas of these two circles to be less than or equal to 5$\pi$. If $r+R=10$, what is the maximum difference in the lengths of the radii?
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