how do you graph y=55-4csc(theta+5)???
Csc(θ+5) is the reciprocal of the sine function. Unless you are very familiar with the function, it may be easier to graph first the sine function, and then graph the reciprocal. The reason is because where there are zeroes in the sine function, it becomes a vertical asymptote in the csc function.
In fact, one side of the asymptote goes to +infinity and the other side to -infinity.
Try it out, and post if you have difficulties.