Hill (6) showed that the largest cap inPG.5; 3/ has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 inAG.5; 3/. Here we show that the size of a cap inAG.5; 3/ is bounded above by 48. We also give an example of three disjoint 45-caps inAG.5; 3/. Using these two results we are able to prove that the Steiner triple systemAG.5; 3/ is 6-chromatic, and so we exhibit the first specific example of a 6-chromatic Steiner triple system.