Find the ordered pair $(a,b)$ of real numbers for which
\[(ax + b)(x^5 + 1) - (5x + 1)\]is divisible by $x^2 + 1.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the ordered pair $(a,b)$ of real numbers for which
\[(ax + b)(x^5 + 1) - (5x + 1)\]is divisible by $x^2 + 1.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
(2,3)
Find the ordered pair $(a,b)$ of real numbers for which
\[(ax + b)(x^5 + 1) - (5x + 1)\]is divisible by $x^2 + 1.$
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