Math Problem Solver

\[ \frac{5}{3} - 5 + 1 = - \frac{7}{3} = -2.\overline{3} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{5}{3}\), \(\frac{-5}{1}\), and \(\frac{1}{1}\) is \(3\). \[ \begin{aligned} \frac{5}{3} - 5 + 1 &= \frac{5 \cdot 1}{3 \cdot 1} + \frac{-5 \cdot 3}{1 \cdot 3} + \frac{1 \cdot 3}{1 \cdot 3} \\ &= \frac{5 + -15 + 3}{3} \\ &= \frac{-7}{3} \end{aligned} \]