After re-watching The Earth King episode, we see that the Council of Five consists of the highest ranking generals in the Earth Kingdom. They of course know there is a war going on with the Fire Nation, and are constantly planning their defenses.
In the same episode, after Long Feng is imprisoned, the Dai Li tell Long Feng that they're still loyal to him, unlike the Council of Five which is loyal to the Earth King.
But, it seems implied that the Council of Five was purposefully not telling the Earth King anything about the war. Instead, they probably discussed all military aspects with Long Feng.
Grand Secretariat Long Feng held the true power over the country through his use of the elite Dai Li forces, and the Council members were forced to answer to him.
Why did the Council of Five comply to Long Feng instead of, you know, exposing him? It wouldn't be hard for a council member to just go the king and tell him that there's a war going on (the king would probably believe them since, you know, they're the military leaders...)
It would seem that the point here is that the Dai Lee are way too powerful, capable of keeping the generals under control. But, they're the generals! They literally got the entire Earth Kingdom's army on their side, which is bound to be greater than the number of Dai Lee agents (since they're probably some kind of elite unit...).