How is the impulse response related to pole/zero-plot?
The impulse response is the inverse Laplace transform of the transfer function. Hence if you know this latter you can get the former. 

If you have a poles-zeros diagram you effectively know the transfer function (neglecting a scale factor). Therefore you can get the general form of the impulse response.

For example, in your case, the transfer function is:

$$
H(s) 
= K \cdot \frac{s}{(s-s_p)(s-s_p^{*})}
= K \cdot \frac{s}{s^2 - (s_p + s_p^{*}) s + |s_p|^2}
$$

where \$s_p = -5 + 8 j\,\$ and \$K\$ is an unspecified scale factor. Inserting the value of the pole, you get:

$$
H(s)
= K \cdot \frac{s}{s^2 + 10 s + 89}
$$