The information given is enough to derive 4 formulae which you solve simultaneouly for a, b, c and d.
1) Since curve passes through (0,5), substitute x=0 and y=5 to find an equation involving a, b, c and d.
2) y'=3ax2+2bx+c
Now there is a turning at (0,5), so when x=0, y'=0. Substitute these...