5. (10 points) A convoy of trucks is delivering supplies to a disaster victim resettlement point. Each truck has a carrying capacity of 10 tons. If each tent is allocated 1.5 tons of supplies, there will be less than one truck's worth of supplies left over. If each tent is allocated 1.6 tons of supplies, there will be a shortage of more than 2 trucks' worth of supplies. How many tents are there at the resettlement point at a minimum?
【Analysis】The number of vehicles and tents at the resettlement point in the two allocation plans in the question is the same. Therefore, let them be $X$ and $Y$ respectively, and set up the corresponding system of inequalities according to the question. First eliminate $Y$ in the system of inequalities, then solve for the solution set of the inequality about $X$, and substitute integer values of $X$ within its solution set back into the original system of inequalities to find the solution set for $Y$.

【Solution】Solution: Let the number of vehicles be $X$ and the number of tents be $Y$. According to the question, we have:
$$
\left\{\begin{array}{l}
10 \times(X-1)<1.5 Y<10 X \\
10 \times(X+2)<1.6 Y<10 \times(X+3)
\end{array}\right.
$$

Eliminating $Y$ gives: $\left\{\begin{array}{l}\frac{100 \times(X-1)}{15}<\frac{100 \times(X+3)}{16} \\ \frac{100 \times(X+2)}{16}<\frac{100 \times X}{15}\end{array}\right.$
Solving this, we get: $30<X<61$
Since we are looking for the minimum number of tents, the number of vehicles should also be the minimum. Therefore, the number of vehicles $X$ should start from the integer 31 and be tried until a value of $Y$ that satisfies the original system of inequalities is found.
(1) Substituting $X=31$ into the original system of inequalities, we get:
$$
\left\{\begin{array}{l}
200<Y<206.7 \\
206.2<Y<212.2
\end{array}\right.
$$

Therefore: There is no solution for $Y$.
(2) Substituting $X=32$ into the original system of inequalities, we get:
$$
\left\{\begin{array}{l}
206.7<Y<213.3 \\
212.2<Y<218.7
\end{array}\right.
$$

Therefore: The minimum integer value for $Y$ is 213.
Answer: The resettlement point has at least 213 tents.