3. If the real numbers $a, b, c, d, e$ satisfy the conditions
$$
\begin{array}{l}
a+b+c+d+e=8, \\
a^{2}+b^{2}+c^{2}+d^{2}+e^{2}=16 .
\end{array}
$$

Determine the maximum value of $e$.
$$
\begin{array}{l}
f(x)=4 x^{2}+2(a+b+c+d) x+\left(a^{2}+b^{2}+c^{2}+d^{2}\right) \\
=(x+a)^{2}+(x+b)^{2}+(x+c)^{2}+(x+d)^{2} \\
\geqslant 0 .
\end{array}
$$

Therefore, $\Delta \leqslant 0$. Solving this, we get $0 \leqslant e \leqslant \frac{16}{5}$.