The intercept at x = 5 is of multiplicity 2. The polynomial is of degree 5, so the zero at x = 5, the only other zero, must use up the rest of the multiplicities. x = 5 must be of multiplicity 3. The zero at x = 5 had to be of odd multiplicity, since the graph went through the x-axis. But the graph flexed a bit (the flexing being that bendy part of the graph) right in the area of x = 5. This flexing is what tells you that the multiplicity of x = 5 had to be more than just 1.
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