Answer:
There are 5! = 120 ways to arrange the people in a line if there are no restrictions.
To count the number of arrangements where each person is standing beside at least one person they originally stood beside, we can use complementary counting. Let's count the number of arrangements in which at least one person is not standing beside anyone they originally stood beside.
Suppose person A is not standing beside anyone they originally stood beside. Person A can be placed in any of the 5 spots in the line. The two people on either side of person A cannot be the two people that person A originally stood beside. This leaves 3 people that can be placed in each of the two remaining spots, for a total of 3^2 = 9 ways to place the remaining two people. Therefore, there are 5*9 = 45 ways to arrange the people in which at least one person is not standing beside anyone they originally stood beside.
The number of arrangements where each person is standing beside at least one person they originally stood beside is the complement of this, which is 120 - 45 = 75.
Therefore, there are 75 ways to arrange the people in a different order so that each person is standing beside at least one person he or she originally stood beside.