5. Given 9 points in space, where no four points are coplanar, a line segment is drawn between every pair of points. These line segments can be colored blue or red, or left uncolored. Find the minimum value of $n$ such that if any $n$ of these line segments are arbitrarily colored red or blue, the set of these $n$ line segments will necessarily contain a triangle with all sides of the same color.
5. The minimum value of $n$ is 33.

Lemma: For a complete graph of order 5, there exists a coloring method for the edges such that the colored graph contains no monochromatic triangles.
As shown in Figure (1), dashed and solid lines represent edges of two different colors, and in this case, there are no monochromatic triangles in the graph.

Proof of the original problem: As shown in Figure (2), the 9 vertices are numbered $1, 2, 3, \ldots, 9$. Among them, vertices $\{1,3\}, \{1,4\}, \{2,3\}, \{2,4\}$ are all connected by edges, and vertices 1 and 2 within the circle are not connected; similarly, vertices in different circles are all connected, while vertices 3 and 4, 5 and 6, 7 and 8 within the same circle are not connected. By the lemma, this graph contains no monochromatic triangles. It is easy to calculate that the number of edges in this graph is $C_{9}^{2} - 4 = 32$, so $n \geqslant 33$.

On the other hand, if the number of colored edges is at least 33, since the total number of edges is $C_{9}^{2} = 36$, the number of uncolored edges is at most 3. If vertex $A_{1}$ is connected by an uncolored edge, remove $A_{1}$ and all edges connected to it; if there is still a vertex $A_{2}$ connected by an uncolored edge in the remaining graph, remove $A_{2}$ and all edges connected to it, and so on. Since the number of uncolored edges is at most 3, at most 3 vertices and the edges connected to them can be removed, leaving at least 6 vertices, with each pair of vertices connected by a red or blue edge. By the conclusion of Example 1 in this lecture, there must be a monochromatic triangle.
In summary, the minimum value of $n$ is 33.