A region is given by x + y ≥ 5, x - y ≤ 3, x ≥ 0 and y ≥ 0…

Step 1. The two slanted lines. Adding $x + y = 5$ and $x - y = 3$ gives $2x = 8$, so $x = 4$ and $y = 1$. The point $(4, 1)$ passes both rules, so it is a corner.

Step 2. The axes. The line $x + y = 5$ meets the $y$ axis at $(0, 5)$. There $0 - 5 = -5 \le 3$ is true, so $(0, 5)$ is a corner. It meets the $x$ axis at $(5, 0)$, but then $x - y = 5$ is more than $3$, so that point fails. The line $x - y = 3$ meets the $x$ axis at $(3, 0)$, but then $x + y = 3$ is less than $5$, so that point fails. It meets the $y$ axis at $(0, -3)$, which has $y < 0$.

Step 3. Count. The corners are $(0, 5)$ and $(4, 1)$: two corner points.

Step 4. Bounded? The point $(10, 10)$ gives $20 \ge 5$ and $0 \le 3$, so it is feasible. Moving further along the line $y = x$ stays feasible, so the region is unbounded.