Why equations with power of 5 and above don't have a way to slove them?
If you mean "why do polynomial equations of degree 5 and higher not have a general method that applies to all such equations" it was proved that there exist such polynomials that have solutions that cannot be written in terms of roots.
See the "Abel-Ruffini theorem": https://en.wikipedia.org/wiki/Abel%E...uffini_theorem
(1) and (3): Multiply it out:
$$(x-a)(x-b)(x-c)(x-d)(x-e) = x^5-(a+b+c+d+e)x^4+(ab+ac+ad+ae+bc+bd+be+cd+ce+de)x^3-(abc+abd+abe+acd+ace+ade+bcd+bce+bde+cde)x^2+(abcd +abce+bcde)x-abcde$$
(2) Any equation with a polynomial on one side of the equation and a constant (or another polynomial) on the other is called a polynomial equation by definition. There is no reason for it other than that is its definition.