If your scale is [5,5,5] then the radius would be 2.5, yes. [5,5,5] are not radius values, but extents of the bounding box (so in the case of a sphere, diameter).
A [1,1,1] particle will have dimensions of 1unit x 1unit x 1unit (assuming it's a scale value applied to a 1x1x1 object). Scale radius is just [max(scale.x, scale.y, scale.z) * 0.5].
A [1,1,1] particle will have dimensions of 1unit x 1unit x 1unit (assuming it's a scale value applied to a 1x1x1 object). Scale radius is just [max(scale.x, scale.y, scale.z) * 0.5].