Let the function $f(x)=x^2$ be defined on the closed interval $[1,5]$. For what value of $c$, $c \in (1,5)$, is the slope of the tangent to the graph of $f$ equal to the slope of the secant line connecting $\left(1,f(1)\right)$ and $\left(5,f(5)\right)$?
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