There are several ways. Quaternions, though more complicated if you dig into their math, present the simpler alternative in terms of lines of code.

With quaternions, you can instantiate a Quaternion object using one of the static methods in the Quaternion class. You mention rotations about specific axes, so we can use the AngleAxis method to create a suitable quaternion. These are then multiplied onto the vector you wish to rotate. The result is the rotated vector. So the example you described above would be:

    Vector3 toBeRotated = new Vector3(0, 5, 0);
    Quaternion rotateVectorAboutX = Quaternion.AngleAxis(30, new Vector3(1, 0, 0));
    Quaternion rotateVectorAboutY = Quaternion.AngleAxis(55, new Vector3(0, 1, 0));

    Vector3 afterRotation = rotateVectorAboutX * rotateVectorAboutY * toBeRotated;

Note that the order must always be Quaternion*Vector, never Vector*Quaternion. I'm not a math wizard, but my guess is that this is related to the dimensionality of their underlying matrix representations. When you multiply matrices, the "connecting" dimensions must match, i.e. [1x4][4x4] is okay, but not [4x1][4x4].

There are plenty other ways to go about this, like EulerAngles, if you're more into that.