To find the number of different ways to arrange 5 plants, we can use the concept of permutations. The number of ways to arrange \( n \) objects is given by \( n! \) (n factorial), which is the product of all positive integers up to \( n \).
So, for 5 plants, we calculate:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \]
Therefore, Bobby can arrange the plants in the planter in \( \boxed{120} \) ways.