Answer
$\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{137}{60}$.
Work Step by Step
We need to sum the first five terms of the sequence whose general term is $a_{n}=\frac{1}{n}$. This yields
$\sum\limits^{5}_{n=1}(\frac{1}{n})=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}$
$=\frac{60}{60}+\frac{30}{60}+\frac{20}{60}+\frac{15}{60}+\frac{12}{60}$
$=\frac{137}{60}$
