An aspheric lens, as focused as it can get, will project an image of your light source. If you have a 20mm ring of ten sources, you can't get more than a tiny fraction of that light concentrated into a 4.8mm diameter spot.
If you REALLY can only have a 4.8mm spot, you will want a large fresnel lens (As big as you can get it) and a bare LED on a heatsink a few meters away. This will project a spot about that small.