Find the coefficient of y^4 in the expansion of (2y - 5 + y^2)^6.
Expand (2y - 5 + y^2)^6:
y^12 + 12 y^11 + 30 y^10 - 140 y^9 - 585 y^8 + 792 y^7 + 4164 y^6 - 3960 y^5 - 14625 y^4 + 17500 y^3 + 18750 y^2 - 37500 y + 15625
