Yes, that's correct. That's the big disadvantage to the topological method I talk about (developed by Vladimir Arnold); it can only prove stuff about the general nth-degree formulas, whereas Galois theory can prove stuff about specific polynomials (e.g., that x^5 – x – 1 is unsolvable in radicals).

On the other hand, the topological method can be easily extended to prove stuff about formulas including other continuous, single-valued operations, like exponential and trigonometric functions, and Galois theory has a harder time with this.