In general, the point-slope form of a linear equation is:
[tex]y-y_1=m(x-x_1)_{}[/tex]Where (x_1, y_1) is a point on the line.
In our problem:
[tex]\begin{gathered} (x_1,y_1)=(5,6),m=\frac{2}{5} \\ \Rightarrow y-6=\frac{2}{5}(x-5) \end{gathered}[/tex]We can simplify more the last expression, but we would lose the point-slope form and obtain the standard form instead.
Thus, the answer is:
[tex]y-6=\frac{2}{5}(x-5)[/tex]