Let the number be 'x', Then its reciprocal is $\frac{1}{x}$

Given that,

$$\begin{gathered} = x\frac{1}{x}=\frac{26}{5} \\ = \frac{x^2+1}{x}=\frac{26}{5} \end{gathered}$$

= 5(x²+1)=26x

= 5x²+5-26=0   [By factorising]

= 5x²-25x-x+5=0

= 5x(x-5)-1(x-5)=0

= (5x-1)(x-5)=0

= x=5 or $\frac{1}{5}$ 

Hence, Option C is correct.