To determine if Juan breaks even on day 5, we need to evaluate the expression he recorded:
\[ 16 + (-16) \]
When we simplify this expression:
\[ 16 + (-16) = 16 - 16 = 0 \]
Since the result of the expression is 0, it indicates that Juan's earnings equal his expenditures for that day. In other words, he earns as much money as he spends.
Therefore, yes, Juan breaks even on day 5 because his total earnings and total spending balance out to zero.