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The problem is that Sage makes sense of "+infinity > finite number" situations. If you use the somehow equivalent following inequation the Sage answer coincide with Wolfram

sage: solve([(4*x+5)/x^3>=4/(x+5)/x], x)
[[x > -5, x <= -1], [x > 0]]

Vincent

The problem is seems to be that Sage makes sense of "+infinity > finite number" situations. If you use Even in the somehow equivalent following inequation where both sides of the Sage answer coincide with Wolframinequality are infinite

sage: solve([(4*x+5)/x^3>=4/(x+5)/x], A = (4*x+5)/(x^2)
sage: B = 4/(x+5)
sage: solve(A >= B, x)
[[x > -5, x <= -1], < -5], [x > 0]]
>= -1]]
sage: solve(A/x^2 >= B/x^2, x)
[[x < -5], [x >= -1]]

Vincent