Approach:

Let's assume that a student needs to score x on the fifth exam.

We will use the following formula for calculating average.

\(\displaystyle{A}{v}{e}{r}{a}\ge={\frac{{{S}{u}{m}\ {o}{f}\ {s}{c}{\text{or}}{e}{s}}}{{{N}{u}{m}{b}{e}{r}\ {o}{f}\ {e}{x}{a}{m}{s}}}}\)

Calculation:

\(\displaystyle{A}{v}{e}{r}{a}\ge={\frac{{{S}{u}{m}\ {o}{f}\ {s}{c}{\text{or}}{e}{s}}}{{{N}{u}{m}{b}{e}{r}\ {o}{f}\ {e}{x}{a}{m}{s}}}}\)

\(\displaystyle{90}={\frac{{{82}+{96}+{91}+{92}+{x}}}{{{5}}}}\)

\(\displaystyle{90}={\frac{{{361}+{x}}}{{{5}}}}\)

\(\displaystyle{90}\times{5}={361}+{x}\)

\(\displaystyle{450}={361}+{x}\)

\(\displaystyle{x}={450}-{361}\)

\(\displaystyle{x}={89}\)

Final Statement:

A student needs to score 89 on the fifth college exam.