In order to find the slope that is parallel to the given line, you first consider that all parallel lines have the same slope.
Moreover, you consider that the general form of the equation of a line is:
y = mx + b
where m is the slope and b the y-intercept.
By comparing with the given equation y = 2/3 x + 5, you can conclude that the slope is m = 2/3.
Hence, the searched slope is 2/3