5. Put four small balls with a radius of 1 into a large ball, then the minimum radius of this large ball is ( ).
(A) $1+\frac{\sqrt{6}}{2}$
(B) $1+\frac{\sqrt{3}}{2}$
(C) $2+\sqrt{6}$
(D) $1+\frac{2 \sqrt{3}}{3}$
5. (A).

Let the radius of the large sphere be $R$, and the small spheres inside the large sphere must be tangent to each other in pairs. The centers of the small spheres form a regular tetrahedron with an edge length of 2, and the center of the tetrahedron $O$ is the center of the large sphere. Let the distance between the center of a small sphere and the center of the large sphere be $a$, then $a=R-1$.
$$
\therefore a=\frac{\sqrt{6}}{2} \text {. Therefore, } R=\left(1+\frac{\sqrt{6}}{2}\right) \text {. }
$$