See graph and explanations.
Work Step by Step
Step 1. Based on the given conditions, we can write the first inequality as $x^2+y^2\leq25$ shown with the red shaded area. Step 2. The second inequality can be written as $x+2y\geq5$ shown with the blue shaded area in the figure. Step 3. The overlapping area (appears in purple) shows the solution for both inequalities.