Answer
$7$
Work Step by Step
The dot product of two vectors $\mathbf a= \langle a_1,a_2,a_3 \rangle$ and $\mathbf b= \langle b_1,b_2,b_3 \rangle$ is $a_1b_1+a_2b_2+a_3b_3$.
So for $\mathbf a= 3i+2j-k=\langle 3,2,-1 \rangle$ and $\mathbf b= 4i+5k=\langle 4,0,5 \rangle$, $$\mathbf a \cdot \mathbf b =3(4)+2(0)+(-1)(5)=12+0-5=7.$$