to solve this we need to multiply and divide by the complex conjugates, so:
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]and now we solve it
[tex]\frac{5\cdot(7+i)}{7\cdot7+7i-7i-i\cdot i}[/tex][tex]\begin{gathered} \frac{35+5i}{49+1} \\ \frac{35}{50}+\frac{5}{50}i \end{gathered}[/tex]So the answer is:
[tex]\begin{gathered} \frac{7}{10}+\frac{1}{10}i \\ or\text{ } \\ 0.7+0.1i \end{gathered}[/tex]