In your opinion, which faction is the strongest in Heroes 5? Let's discuss the advantages and disadvantages of each faction.

Well...
Gnomes are good when defending their own Castle.

That's undeniable. But Phoenixes and Vampires are quite effective when attacking Gnomes.

They have the following abilities:
Pillage (which makes life easier), Mentorship, Eternal Light, Pyrokinesis, Diversion, which is useful against Mages and Necromancers, especially considering they also have Keen Mind, so it's a fairy tale, Empathy, and Rune Harmony.

Their abilities are indeed the best in the game, but their units are not. However, Pillage and Keen Mind come from Logistics, which has only a 2% chance of being obtained. Mentorship is a 3rd-tier ability, so it's not always easy to get, just like Empathy. Rune Harmony is often completely useless, considering the presence of Leadership. Pyrokinesis and Eternal Light are very strong, but if you take all of the above, you'll be left without Attack and Defense.

Mages are also good when they have a lot of mana, and of course, it is assumed that they will level up.

Exactly, level up. Who will let them? In the current state of affairs, they need to be killed almost first.

Dark Elves:
To have mana, they need: Mana Drain and also Mana Regeneration, and Arcane Knowledge.

And they also really need Chaos Magic, Attack, and Luck. You can't get enough levels. And prolonging the game is risky.

Necromancers don't have a mana source, except for Spiritual Link.

And that's all they need. 1 mana for every 10 units of damage dealt is a lot. Especially considering that Mana Drain is also not difficult to obtain.