Step 1: A quadratic polynomial with given sum and product of zeroes is
$$p(x)=x^{2}-(\text{sum})x+(\text{product})$$
Step 2: Substitute sum $=5$ and product $=-6$.
$$p(x)=x^{2}-5x-6$$
Step 3: Put $p(x)=0$ and split the middle term ($-5=-6+1$ and $-6\times 1=-6$).
$$x^{2}-6x+x-6=0$$
Step 4: Group the terms.
$$x(x-6)+1(x-6)=0 \;\Rightarrow\; (x-6)(x+1)=0$$
Step 5: Therefore
$$x=6 \quad\text{or}\quad x=-1$$
Step 6: Verification: sum $=6+(-1)=5$ ✓ and product $=6\times(-1)=-6$ ✓
Hence the polynomial is $x^{2}-5x-6$ and its zeroes are $6$ and $-1$.