The sum of Emily's quiz scores so far is $92+95+87+89+100=463$.
To find the score she needs on the sixth quiz, we can set up the equation: 
\[\frac{463+x}{6}=93\]
where $x$ is the score she needs on the sixth quiz.
Solving for $x$, we have $463+x=558$, so $x=558-463=95$.
Therefore, Emily needs to get a score of $\boxed{95}$ on the sixth quiz to make the arithmetic mean of the six scores equal 93.
The answer is: 95
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Emily's quiz scores so far are: 92, 95, 87, 89 and 100. What score does she need to get on the sixth quiz to make the arithmetic mean of the six scores equal 93?

### Answer:
