Solving system of equations with Root

I have this system of equations. I want to express all variables in terms of x as you can see. x is a parameter.

Solve[{y (z - x) == x^6, x zg - z zg == x z^2 za zb - x z za zb zg, 
za zg - zb zg == z za zb - z za^2 zb, zb - zg == z za zb - z zb^2, 
za zb (z - zg) == zg (-zb + zg), za > 0, zb > 0, zg > 0, z > 0}, {y, za, zb, zg, z}, Reals]

However Mathematica doesn't know how to solve it. Solutions show me something called Root and I can't make sense out of any of the expressions I get. What I get is:

y -> ConditionalExpression[((
x^6)/(-x + 
Root[-x + 
2 x^2 + (1 - 3 x - x^2) #1 + (1 + 2 x - 4 x^2) #1^2 + (-1 + 
 5 x - x^2) #1^3 + (-1 + x - x^2) #1^4 + x^2 #1^5 &, 3]))

I also tried using reduce which gives me a set of solutions for y:

y == Root[

x^26 + (-x^18 + x^19 - x^20 + 5 x^21) #1 + (-x^12 + x^13 + 3 x^14 - 
   4 x^15 + 10 x^16) #1^2 + (x^6 - x^7 + 5 x^8 + 3 x^9 - 6 x^10 + 
   10 x^11) #1^3 + (1 - x + 3 x^3 + x^4 - 4 x^5 + 
   5 x^6) #1^4 + (-1 + x) #1^5 &, 1] 

I've read this thread: How do I work with Root objects? but it doesn't solve my problem since I have this free parameter x that ruins everything. For example if I try ToRadicals or numerical value I don't get anything. How do I make sense of it? How can I proceed to get the full expression for y in terms of x without Root? I tried FindInstance but it doesn't work in my case since I have this free parameter x. If this helps I'm only interested in y, the rest of the parameters don't really matter. Any help is greatly appreciated.

Answer

From a comment, it seems maybe the OP would like to rationalize the expression:

Product[y - 
   Root[x^26 + (-x^18 + x^19 - x^20 + 5 x^21) #1 + (-x^12 + x^13 + 

         3 x^14 - 4 x^15 + 10 x^16) #1^2 + (x^6 - x^7 + 5 x^8 + 
         3 x^9 - 6 x^10 + 10 x^11) #1^3 + (1 - x + 3 x^3 + x^4 - 
         4 x^5 + 5 x^6) #1^4 + (-1 + x) #1^5 &, i], {i, 
   5}] // FullSimplify
(*
(1/(-1 + x))(x^26 + x^18 (-1 + x - x^2 + 5 x^3) y + 
  x^12 (-1 + x (1 + x (3 + 2 x (-2 + 5 x)))) y^2 + 
  x^6 (1 + x (-1 + x (5 + x (3 + 2 x (-3 + 5 x))))) y^3 + (1 - x + 
     3 x^3 + x^4 - 4 x^5 + 5 x^6) y^4 + (-1 + x) y^5)
*)

Set this equal to zero to represent the locus. Note that the product may or may not have introduced extraneous solutions.

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Addendum

Silly me, this is equivalent to, with less work, the following:

First[
  Root[x^26 + (-x^18 + x^19 - x^20 + 5 x^21) #1 + (-x^12 + x^13 + 
        3 x^14 - 4 x^15 + 10 x^16) #1^2 + (x^6 - x^7 + 5 x^8 + 
        3 x^9 - 6 x^10 + 10 x^11) #1^3 + (1 - x + 3 x^3 + x^4 - 
        4 x^5 + 5 x^6) #1^4 + (-1 + x) #1^5 &, 1]

  ]@y
(*
x^26 + (-x^18 + x^19 - x^20 + 5 x^21) y + (-x^12 + x^13 + 3 x^14 - 
    4 x^15 + 10 x^16) y^2 + (x^6 - x^7 + 5 x^8 + 3 x^9 - 6 x^10 + 
    10 x^11) y^3 + (1 - x + 3 x^3 + x^4 - 4 x^5 + 5 x^6) y^4 + (-1 + 
    x) y^5
*)

There is still the general caveat about rationalizing leads potentially to extraneously solutions.