Since (0,0) satisfies tan(5x-y)=5x, the graph passes through the origin.
tan(5x-y) is undefined when 5x-y=(2n+1)π/2 that is, an odd number of right angles, because tan((2n+1)π/2) is undefined (infinite). So 5x-y=(2n+1)π/2 represents an infinite series of asymptotes as integer n increases or decreases. A curve exists between each consecutive pair of asymptotes.
Each of the curves intersects the y-axis (x=0) when tan(-y)=0⇒y=nπ, so now we know that each of the separate curves of this graph has y-intercepts which are π units apart.
The x-intercepts also occur periodically. These are the solutions for tan(5x)=5x. As x increase positively or decreases negatively, the x-intercepts become closer to where the asymptote intercepts the x-axis, which is x=(2n+1)π/10. At the origin we have the first x-intercept (n=0), which lies between the asymptote intercepts at(-0.1π,0) (n=-1) and (0.1π,0) (n=0). The second x-intercept must be close to 0.3π (0.94 approx). In fact it's around 0.9. The next x-intercept is close to ½π (1.57 approx) at around 1.55.
These are some interesting facts about the graph tan(5x-y)=5x.