Interpolating Polynomial

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I need help with this.

Find a polynomial of degree 4 of the form $f(x)=ax^4+bx^3+cx^2+dx+e$.

Plot points $(1,7),(2,2),(3,9),(5,1)$, and $(7,5)$.

Thank you.

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Hint: From the first given point, you get $f(1)=a+b+c+d+e=7$. Proceeding like this gives you five linear equations in five unknowns ($a,b,c,d, \text{ and } e$). Solve the system to find $a,b,c,d,e$.