+2862 .I literally just watched a video on how to do this, this is a learning process for me too 
I am assuming that you learned the trig vocabulary for this as you asking these problems
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Lets first do a cosine graph cuz its easier
This is the base equation for a cosine graph:
\(y=A\cos{b}(x-h)+c\)
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So first find the amplitude, which is the height of the waves of the graph. (using y-values)
\(\text{Amplitude}=|\frac{\text{Max}-\text{Min}}{2}|\)
\(|\frac{-5-(-4)}{2}|\)
\(|\frac{-1}{2}|\)
\(\text{Amplitude}=\frac{1}{2}\)
Now we have the "A" value
\(y=\frac{1}{2}\cos{b}(x-h)+c\)
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Ok now we have to find the period
We first find the positive difference of the x values to find the horizontal distance.
\(|-1-3.5|=4.5\)
Then we double what we got
\(9\)
Then we solve for the b-value
\(9=\frac{2\pi}{b}\rightarrow9b=2pi\rightarrow{b}=\frac{2pi}{9}\)
Now we have
\(y=\frac{1}{2}\cos{\frac{2pi}{9}}(x-h)+c\)
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Now we have to find the phase shift (h-value)
Since it has shifted -1, ( coordinate (-1, -5) tells us that. )
We now have:
\(y=\frac{1}{2}\cos{\frac{2pi}{9}}(x+1)+c\)
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Now we have to find the vertical shift (c-value)
Formula for that is
\(c=\frac{\text{Maximum}}{2}\)
\(c=\frac{-5+(-4)}{2}\)
\(c=-4.5\)
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So the equation of the sinusoidal graph is
\(y=\frac{1}{2}\cos{\frac{2pi}{9}}(x+1)-4.5\)
This is the cosine graph.
This is the video I learned from, if you want to find the sine graph, follow the steps in the video.
