Given $a_{n}=\displaystyle\sum_{k=1}^{n}\;\sqrt{1+\large\frac{1}{k^2}+\large\frac{1}{(k+1)^2}}\;$ the value of $\;a_{5}\;$ is

Question

$(a)\;35\qquad(b)\;\large\frac{35}{6}\qquad(c)\;36\qquad(d)\;6$