Nope, it’s theoretical maps, and the thing you’re missing is that your intuition plays tricks on you. Go ahead and try it. Draw out a map. Then color it in as best you can.
LOL! Since Cecil was of no help, I found other sites that explained two things to me. One, theoretical maps count. Two, my efforts at creating maps requiring five colors were futile, and when I thought I had one it was because I was using a color unnecessarily.
Two points to remember:
(i) In real maps, the sea is painted blue and no land masses can be coloured that shade. These restrictions do not apply in the 4-colour theorem.
(ii) In real maps, separate parts of one country must be the same colour. Again, this does not apply in the theorem.
With these restrictions, I would recommend Achernar’s advice. Try and construct a counterexample.