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Indeed, in Heroes 5, Summoning Magic has a special, unique significance, and the summoned Phoenix is its gem, I would even say its highlight. In my opinion, the Phoenix was created to introduce a certain power balance in the battle between a Warrior and a Mage. After all, Heroes are meant not only to crush enemies with a sword but also to strike them with magic. Although I agree that there are situations where Summoning determines the outcome of the battle (including your example), sometimes it is simply impossible to fight against an army with a Phoenix and there is nothing to counter it with. So many arguments have been made about Dwarves – they were called cheaters, and people talked about imbalance, but it turned out that they couldn't cope with the Phoenix. Personally, I know only a couple of tricks that can help reduce its damage. The first method is well known – it is the Withering Grip of the Death Knights for Necromancers. One such ability allows them to be used effectively in battle. The main thing is to protect these "reapers" and keep them away from both enemy attacks and the Phoenix itself. The second point is Counterspell – with its help, you can not even fight the annoying bird on the battlefield, but simply prevent it from being summoned (however, this method is very expensive, as you will have to pay double mana). And, finally, the third trick consists of a special hero skill called Elemental Equilibrium. Its meaning is that in response to the enemy's Phoenix, exactly the same Phoenix (stats, damage, HP) is automatically summoned on your side – and then it's just a matter of technique...
I don't think I missed anything and I don't seem to have made any mistakes!)) I only have one question regarding the effect of Banish on the Phoenix – I cannot provide any specific information about this. And, of course, if you already have huge armies, the Phoenix itself will no longer have such a fatal effect, as it will be quickly defeated.
P.S.: In the post, I meant specifically summoned Phoenixes, and not hired ones, because the latter do not "grow" with the hero's level...
P.S.S.: And also, if the war turns out to be short, you can try to deprive the enemy hero of mana for the expensive Phoenix using Imps – it's naive, but it might work, and in general, it will be very convenient to attack it with Demons with a Slaying Sword