Aside the fact that I recognize the question in its latex code was completely upside down. I fixed now. I hope is fine.

Now

\(a_1=1
\)

If n =1 then \(a_2=1+\frac{1}{a_1}=1+1=2\)

If n=2 then \(a_3=1+\frac{1}{a_2}=1+\frac{1}{2}=\frac{3}{2}\)

If n=3 then \(a_4=1+\frac{1}{a_3}=1+\dfrac{1}{\frac{3}{2}}=1+\frac{2}{3}=\frac{5}{3}\)

If n=4 then \(a_5=1+\frac{1}{a_4}=1+\dfrac{1}{\frac{5}{3}}=1+\frac{3}{5}=\frac{8}{5}\)

A \(\frac{5}{3}>\frac{3}{2}\) Correct

B \(\frac{8}{5}>\frac{5}{3}\) Incorrect

C. \(a_5=\frac{8}{5}\) Correct