Let's solve the expression step by step:

Given expression:

$-\dfrac{3}{5} + \dfrac{1}{3}$

1. To add these fractions, find a common denominator. The least common denominator (LCD) of 5 and 3 is 15.

2. Convert each fraction to have the denominator of 15:

$-\dfrac{3}{5} = -\dfrac{3 \times 3}{5 \times 3} = -\dfrac{9}{15}$

$\dfrac{1}{3} = \dfrac{1 \times 5}{3 \times 5} = \dfrac{5}{15}$

3. Now add the fractions:

$-\dfrac{9}{15} + \dfrac{5}{15} = \dfrac{-9 + 5}{15} = \dfrac{-4}{15}$

So, the final answer is:

$-\dfrac{4}{15}$

Would you like more details or have any questions about the process? Here are some related questions:

1. How do you determine the least common denominator?
2. What is the procedure for converting fractions to a common denominator?
3. Why is the order of operations important when working with fractions?
4. How do you add fractions with different signs?
5. Can fractions with different denominators be added directly?

Tip: When adding or subtracting fractions with different denominators, always find the least common denominator to simplify the process.