Chapter 2: Limits and Continuity - Section 2.3 - The Precise Definition of a Limit - Exercises 2.3 - Page 65: 1

$\delta=2$

See graph; we can find $|c-a|=|5-1|=4$ and $|c-b|=|5-7|=2$. We choose $\delta=2$ (smaller of the two values) so that for all $x$, when $0\lt|x-c|\lt\delta$, we have $a\lt x\lt b$ as can be seen from the figure.