Shannon, Laura, and Tasha found a shirt which came in five colors at their favorite store, and they each bought one of each color of that shirt. On Monday, they all wear one of their new shirts to work. What is the probability that Shannon, Laura, and Tasha will not all be wearing the same color shirt that day?

$\text{(A) }\frac{12}{25}\qquad\text{(B) }\frac{16}{25}\qquad\text{(C) }\frac{21}{25}\qquad\text{(D) }\frac{22}{25}\qquad\text{(E) }\frac{24}{25}$
1. First, we need to determine the total number of possible outcomes for the colors of shirts that Shannon, Laura, and Tasha can wear. Since each of them has 5 different colors to choose from, the total number of possible outcomes is:
   \[
   5 \times 5 \times 5 = 125
   \]

2. Next, we need to calculate the number of favorable outcomes where Shannon, Laura, and Tasha do not all wear the same color shirt. To do this, we first calculate the number of outcomes where they all wear the same color shirt. Since there are 5 colors, there are 5 such outcomes:
   \[
   \text{(Shannon, Laura, Tasha all wear the same color)} = 5
   \]

3. The number of outcomes where Shannon, Laura, and Tasha do not all wear the same color shirt is then:
   \[
   125 - 5 = 120
   \]

4. The probability that Shannon, Laura, and Tasha will not all be wearing the same color shirt is the ratio of the number of favorable outcomes to the total number of possible outcomes:
   \[
   \frac{120}{125} = \frac{24}{25}
   \]

The final answer is $\boxed{\frac{24}{25}}$