Answer
$\approx 343.2693$
Work Step by Step
The interval [a,b] is subdivided into n intervals,
f is a continuous function over [a,b],
Left Riemann sum $=\displaystyle \sum_{k=0}^{n-1}f(x_{k})\Delta x$
$=[f(x_{0})+f(x_{1})+\cdots+f(x_{n-1})]\Delta x$,
where $a=x_{0} < x_{1} < \cdots < x_{n}=b$
are the endpoints of the subdivisions,
and $\displaystyle \Delta x=\frac{b-a}{n}$.
-----------------
$f(x)=e^{-x},\ \ [a,b]=[-5,5],\ \ n=5$
$\displaystyle \Delta x=\frac{b-a}{n}=\frac{10-0}{5}=2$
$\left[\begin{array}{lllllll}
k & 0 & 1 & 2 & 3 & 4 & 5\\
x_{k} & -5 & -3 & -1 & 1 & 3 & 5\\
f(x_{k}) & e^{5} & e^{3} & e^{1} & e^{-1} & e^{-3} & ...
\end{array}\right]$
Left Riemann sum $=$
$=(e^{5}+e^{3}+e^{1}+e^{-1}+e^{-3})\cdot 2$
$\approx 343.2693$
