Covered!

Because $3^2 + 5^2<7^2$ , we see that the angle facing the side of lenght $7$ is obtuse. That means that the whole triangle can be covered by a circle of diameter $d=7$ . Of course such a circle also has to cover the side of lenght $7$ , and therefore the minimum radius of the circle is equal to $\frac{1}{2} d= r= \boxed{3.5}$ .