Several of the rational zeroes are factors of 20: 1, 20, 4, 5.
Other rational zeroes are ⅕, ⅘, because the factors of the leading coefficient 5 are 1 and 5.
There are a further six rational zeroes formed by negating the six positive ones.
When we plug each of those into f(x) we discover f(4)=0, making x=4 a true zero.
Now divide by this zero:
4 | 5 -14 -19 -20
5 20 24 | 20
5 6 5 | 0 = 5x2+6x+5.
To find the other (complex) zeroes use the quadratic formula:
x=(-6±√(36-100))/10=(-6±√-64)/10=-⅗±⅘i.
The zeroes are: 4, -⅗+⅘i, -⅗-⅘i.