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.