#### Answer

$k=3$

#### Work Step by Step

We start with the given equation: $5k+2(k+1)=23$
We apply the distributive property to simplify the left side of the equation: $5k+2k+2=23$
We subtract $2$ from both sides of the equation and combine like terms: $$5k+2k+2-2=23-2$$$$7k=21$$
We divide by $7$ on each side of the equation: $$\frac{7k}{7}=\frac{21}{7}$$$$k=3$$