How to find the minimum value of one variable in two functions using Mathematica?

How do I find the minimum value which satisfies the two equation below by using Mathematica? d and w in these equations are constant. The only variable is a.

y=-5 a^3
y=-a ((5 w d^2)/4 + 5 w d) + (5 w d^2)/2


I typed this into Mathematica but it is not working

MinValue[{-5 a w^2, (5 w d^2)/2 - a (5 w d + (5 w d^2)/4)}, {a}]


If I understand your question, what you want to minimize is the value of a subject to the constraint of the equations. If so, the correct syntax is
MinValue[{a, -5 a w^2 == (5 w d^2)/2 -