Anytime you change a function from f(x) to f(x)+k, you are making a vertical shift. In fact, in the old function you associated with every x the y-value f(x). Now, you're associating with every x the new value f(x)+k, which is the old value with an additional constant. This means that you're changing the y value, from the old y_0=f(x) to the new y_1=f(x)+k. And as you can see, y_1=y_0+k.
So, if k is positive, you're making the new y bigger than the older, which means that the point (x,y_1) is above the old point (x,y_0). Otherwise, if k is negative, the new point is below the old one.
So, in this case, you have the old function y=sin(x) that associates with every x the value sin(x), and you're changing it with the new function y=sin(x)+5.
This new function works exactly like the old one, but it adds five extra units to the old value, which means that the graph is shifted upwards.
