The equation of a line parallel to the given line y=\frac{7}{9}x+5 will also have a slope of \frac{7}{9} but may have a different y-intercept.
Therefore, the equation of a line parallel to y=\frac{7}{9}x+5 is of the form y=\frac{7}{9}x+b where b is the y-intercept.
\therefore The equations that are parallel to the line y=\frac{7}{9}x+5 are of the form y=\frac{7}{9}x+b, where b can take any real value.
\therefore \boxed{y=\frac{7}{9}x+b} where b is any real number.