Answer
$S_{1}=1;$
$S_{2}=S_{1}+\dfrac {1}{4}=\dfrac {5}{4};$
$S_{3}=S_{2}+\dfrac {1}{9}=\dfrac {49}{36};$
$S_{4}=S_{3}+\dfrac {1}{16}=\dfrac {205}{144};$
$S_{5}=S_{4}+\dfrac {1}{25}=\dfrac {5269}{3600}$
Work Step by Step
$S_{n}=1+\dfrac {1}{4}+\dfrac {1}{9}+\dfrac {1}{16}+\dfrac {1}{25}\Rightarrow $
$S_{1}=1;$
$S_{2}=S_{1}+\dfrac {1}{4}=\dfrac {5}{4};$
$S_{3}=S_{2}+\dfrac {1}{9}=\dfrac {49}{36};$
$S_{4}=S_{3}+\dfrac {1}{16}=\dfrac {205}{144};$
$S_{5}=S_{4}+\dfrac {1}{25}=\dfrac {5269}{3600}$
