Maximum number of intersection points of 5 non parallel distinct lines in $a$ plane are ________.

Step 1 (Maximum Intersections Condition): The maximum number of intersection points of distinct lines in a plane occurs when:

1. No two lines are parallel (every pair of lines intersects at exactly one point).

2. No three lines are concurrent (no point is shared by three or more lines).

Step 2 (Apply Combinations): Under these conditions, every choice of 2 lines out of $n$ distinct lines yields exactly 1 unique intersection point. Therefore, the maximum number of intersection points for $n$ lines is:

Step 3 (Substitute n = 5):

Step 4 (Conclusion): The maximum number of intersection points is exactly 10.