1. **State the problem:** Calculate the value of $5 \frac{3}{7} - 2$. 2. **Convert the mixed number to an improper fraction:** $$5 \frac{3}{7} = \frac{5 \times 7 + 3}{7} = \frac{35 + 3}{7} = \frac{38}{7}$$ 3. **Rewrite the subtraction with fractions:** $$\frac{38}{7} - 2$$ 4. **Convert the whole number 2 to a fraction with denominator 7:** $$2 = \frac{2 \times 7}{7} = \frac{14}{7}$$ 5. **Perform the subtraction:** $$\frac{38}{7} - \frac{14}{7} = \frac{38 - 14}{7} = \frac{24}{7}$$ 6. **Convert the improper fraction back to a mixed number:** $$\frac{24}{7} = 3 \frac{3}{7}$$ **Final answer:** $3 \frac{3}{7}$