Newtonian n-body problem is an old, complicated problem. It is very significant to study it. Even about three problem, the completed solutions have not obtained so far. It is one hottest point studied in n-body problem. Based on some hypothesis of symmetric conditions, some necessary and sufficient conditions have been obtained with the purely algebra method. The classification of planar 5 - body central configurations is discussed , in which three class planar 5 -body central configurations are obtained.