To find the score Deon needs on his next test to achieve an average of 78, we can set up the following equation.
Let \( x \) be the score that Deon needs on his next test. The average of his scores including the next test will be given by:
\[ \frac{97 + 87 + 76 + 58 + x}{5} = 78 \]
First, we calculate the sum of his current scores:
\[ 97 + 87 + 76 + 58 = 318 \]
Now we substitute this sum into our equation:
\[ \frac{318 + x}{5} = 78 \]
Next, we multiply both sides of the equation by 5 to eliminate the fraction:
\[ 318 + x = 390 \]
Now, we solve for \( x \) by subtracting 318 from both sides:
\[ x = 390 - 318 \] \[ x = 72 \]
Therefore, Deon needs to score 72 on his next test to have an average of 78.