Embedding 5-cycle systems into pentagon triple systems

We show that the spectrum for pentagon triple systems is the set of all n≡1,15,21n≡1,15,21 or 25(mod30). We then construct a 5-cycle system of order 10n+110n+1 which can be embedded in a pentagon triple system of order 30n+130n+1 and also construct a 5-cycle system of order 10n+510n+5 which can be embedded in a pentagon triple system of order 30n+1530n+15, with the possible exception of embedding a 5-cycle system of order 21 in a pentagon triple system of order 61.