probability - What are the chances of getting at least 3 fours when rolling 5 dice?

What are the chances of getting at least three or more "fours" or higher number when rolling a fair six-sided die five times?

Actually, this is a problem I am curious about the answer and I can't find it anywhere. I would be glad if explained.

The question can be generalized to getting at least $A$ times a number $B$ or higher when rolling $C$ dice of $D$ sides. I would like to know the function that returns this probability given $A$, $B$, $C$ and $D$ parameters.

Examples of success: $(1,4,4,3,4)$, $(2,6,4,3,5)$, $(6,1,5,5,4)$;

Examples of failure: $(3,4,4,1,1)$, $(6,5,1,2,1)$, $(5,1,4,3,3)$.

Thanks.