1. The problem is to subtract the mixed number $-5 \frac{7}{15}$ from the decimal $-5.52$. 2. First, convert the mixed number $-5 \frac{7}{15}$ to an improper fraction or decimal for easier subtraction. 3. Convert $\frac{7}{15}$ to decimal: $$\frac{7}{15} = 0.4666\ldots$$ 4. So, $-5 \frac{7}{15} = -5.4666\ldots$ 5. Now subtract: $$-5.52 - (-5.4666\ldots) = -5.52 + 5.4666\ldots$$ 6. Perform the addition: $$-5.52 + 5.4666\ldots = -0.0533\ldots$$ 7. Rounded to four decimal places, the result is $-0.0533$. 8. Therefore, $$-5.52 - \left(-5 \frac{7}{15}\right) = -0.0533$$