AT-OEMO-BEG 2014 Problem 2

All empty white triangles in figure are to be filled with integers such that for each gray triangle the three numbers in the white neighboring triangles sum to a multiple of $5$ . The lower left and the lower right white triangle are already filled with the numbers $12$ and $3$ , respectively. Find all integers that can occur in the uppermost white triangle.

(G. Woeginger, Eindhoven, The Netherlands)