What is the smallest integer $n$ for which $5+3 n$ is larger than 300 ?
The inequality $5+3 n>300$ is equivalent to $3 n>295$, which is equivalent to $n>\frac{295}{3}$.

Since $\frac{295}{3}=98 \frac{1}{3}$, then this is equivalent to $n>98 \frac{1}{3}$.

Therefore, the smallest positive integer $n$ for which $5+3 n>300$ is $n=99$.

ANSWER: 99