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Fundamental theorem of algebra tells you the maximum number of real solutions there are to a polynomial equation.
In your example, the highest exponent on x is 5, so there will be at most 5 real solutions.
The other thing to consider is that not only are there a maximum of 5 real solutions, there are guaranteed 5 solutions total (though some of them may be imaginary).
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If you have multiple choice options, you don't need to solve it. You choose the only one that makes sense.
It's a fifth degree polynomial, that means it has 5 roots; which of those options shows 5 roots?
ok, bu then then how would that work out for my next equation:
x3 – x2 + 5x – 5 = 0
(c) is unclear. What are the solutions there?
(a) and (b) are plausible. The only difference is 1 or -1, so you could test those to see which on is a root.
Ok, well testing x=1 and x=-1 will still narrow it down. If x=1 is a root then it has to be (a).
If -1 works, then you can factor it out (use synthetic division or whatever).
Also, this polynomial is factorable, which will show the solutions right away.