Х+1/5=5 3/5

To solve the equation \(x + \frac{1}{5} = 5 \frac{3}{5}\), we need to isolate \(x\).

Step 1: Convert the mixed number \(5 \frac{3}{5}\) to an improper fraction: \[5 \frac{3}{5} = \frac{5 \times 5 + 3}{5} = \frac{25 + 3}{5} = \frac{28}{5}\]

Step 2: Substitute the improper fraction back into the equation: \[x + \frac{1}{5} = \frac{28}{5}\]

Step 3: To eliminate the fraction on the right side, multiply through by 5: \[5x + 1 = 28\]

Step 4: Subtract 1 from both sides to isolate \(5x\): \[5x = 27\]

Step 5: Finally, divide both sides by 5 to solve for \(x\): \[x = \frac{27}{5} = 5 \frac{2}{5}\]

Therefore, the solution to the equation is \(x = 5 \frac{2}{5}\).