5. At least how many circles with a radius of 1 are needed to cover a circle with a radius of 2.
Let $O$ be the center of a circle with radius 2, and let $A B C D E F$ be a regular hexagon inscribed in the circle (Figure 8). The side length of the hexagon is 2. Construct six circles with the sides of the hexagon as diameters. The intersection points of these six circles, other than $A, B, C, D, E, F$, are denoted as $A_{1}, B_{1}, C_{1}, D_{1}, E_{1}, F_{1}$. These points are the vertices of a regular hexagon with side length 1. Use the above circles with radius 1 to cover the circle with radius 2. The remaining part (the shaded part in Figure 8) is contained within the hexagon $A_{1} B_{1} C_{1} D_{1} E_{1} F_{1}$, and can be completely covered by a circle with center $O$ and radius 1. Therefore, 7 circles can cover the circle with radius 2.

On the other hand, each small circle can only cover one-sixth of the large circle, so at least six circles are needed to cover the large circle. However, these six small circles still cannot cover the point $O$, so at least seven small circles are needed to cover the large circle.