If average test scores are 89 and then a sixth score is 95 what new average?

Let the five original test scores be $s_1, s_2, s_3, s_4, s_5$. The average of these scores is 89, so we have:

$\frac{s_1 + s_2 + s_3 + s_4 + s_5}{5} = 89$

This means the sum of the five scores is:

$s_1 + s_2 + s_3 + s_4 + s_5 = 5 \times 89 = 445$

Now, a sixth score of 95 is added. The sum of the six scores is:

$445 + 95 = 540$

The new average is the sum of the six scores divided by 6:

$\frac{540}{6} = 90$

The new average is $\boxed{90}$.