This system was solved in May 2020, using solveSystem in Macaulay2 v1.15 with an Intel(R) Core(TM) i5-4258U CPU at 2.40GHz.
There were 6 solutions found in 1.24877 seconds (with a Bezout bound of 108).
Reference: Keith Meintjes and Alexander P. Morgan, "Chemical equilibrium systems as numerical test problems", ACM Toms, Vol 16, No 2, 143-151, 1990.
See also: http://homepages.math.uic.edu/~jan/Demo/chemequ.html
i1 : chemequ(CC_53)
2 2
o1 = {y y + y - 3y , y y + 2y y + .000001923y + .00054518y y +
1 2 1 5 2 3 1 2 2 2 3
------------------------------------------------------------------------
2 2
.000034074y y + y + 4.4975e-7y - 10y , 2y y + .00054518y y + .386y
2 4 1 2 5 2 3 2 3 3
------------------------------------------------------------------------
2 2
+ .00041062y - 8y , .000034074y y + 2y - 40y , y y + y y +
3 5 2 4 4 5 2 3 1 2
------------------------------------------------------------------------
2 2 2
9.615e-7y + .00054518y y + .193y + .000034074y y + y + y +
2 2 3 3 2 4 4 1
------------------------------------------------------------------------
4.4975e-7y + .00041062y - 1}
2 3
o1 : List
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The object chemequ is a method function.