This is my idea of the DMC5 scenario that would fill the spaces of the series.

It starts before DMC3 when Vergil was still studying Sparda's life to know the secrets of his power. He was disappointed by Dante  who refused to help him open the gate of the underworld to retrieve Force Edge so he  decided to find someone else who has the power of Sparda. His investigation led him to a man who fought once alongside with Sparda. that man had disappeared after what happened to Sparda's wife and children so Vergil assumed that the man was protecting something other than his life because such a man doesn't fear losing his life. Vergil headed to fortuna looking for that man because he knew that fortuna was the best sanctuary for Sparda's followers. When Vergil reached fortuna he found out that the man died a short while ago. that was another letdown for Vergil. That man had a son (Nero) but he kept his birth a secret to protect him from what happened to Sparda's sons. Vergil realized that story when he saw the mans wife leaving a child at the door of the orphanage just a short while before her death. "that explains why the man was secretive" Vergil thought.Vergil activated Nero's inner strengh by making a small cut in his right arm using yamato but that would take many years to complete. Nero was Vergil's plan B to return to the human world if something went wrong in his quest to retrieve Force Edge from the underworld. After that, vergil left fortuna and found temen-ni-gru.

At the end of DMC3 vergil decided to stay in the demon world to know more secrets about Sparda. during his battle with Vergil, Mundus used Yamato to open the hell gate in fortuna. Vergil managed to take Yamato back then he broke it and threw it in the human world through that gate. the gate was immediately closed and Mundus couldn't escape.
The reason why Vergil prevented Mundus from reaching the human world was that he didn't want Mundus to become even more powerful. Vergil wanted to become the most powerful demon in the underworld and sealing Mundus seemed to be the best action to take at that time. losing Yamato cost Vergil the battle and he fell under the control of a servant of mundus named Nelo Angelo.

When Nelo Angelo was defeated by Dante, Vergil started to break free out of the power of Mundus. He threw his amulet to Dante just before he was thrown back into the demon world because he wanted Mundus to pay for what he had done to him even if that means Dante would have the amulet. In the demon world, Vergil was able to free himself from the servant of Mundus but the power of that demon was only sealed not destroyed.

After a few years agnus's research unsealed the power of Nelo Angelo which was now under control. Agnus thought it was Vergil's power and tried to resurrect Yamato using it but it didn't work. Nero managed to resurrect Yamato because his arm was generally created by that sword.

During those years, Vergil travelled all the underworld seeking the source of Sparda's power but he never tried to kill Mundus who was sealed and weakened because he believed that killing Mundus means giving  another demon the chance to gain control of Mundus's power and become even stronger the same way Arkham tried to control Sparda's power. "That's why Sparda didn't kill Mundus" Vergil said to himself. Vergil never thought of killing Mundus and taking over his power because he believed that Sparda's power was much greater.

Now all of the above must be explained through the DMC history or the unlockable videos because I don't want the game to be all about Vergil.

The game starts with Dante. After defeating Argo Sax at the end of DMC2, Dante heads to the place which was used by his father to return to the human world. Unlike Vergil, Dante knows the way Sparda used to return to the human world. He faces countless demons in his journey and travels deeper into the underworld. Dante's journey leads him to a place that Vergil uses as a base.In that place was the gate Sparda used to return to the human world. They were both shocked to see each other alive. Dante expected another battle with Vergil but Vergil had no reason to fight him this time. Vergil was planning to kill a demon who wants to kill mundus and take over his power to become the new dark emperor. when Dante knew that from Vergil, he didn't care and tried to open the gate to the human world but when Vergil told him why that demon had to be stopped, Dante decided to track that demon. (This journey is Dante's missions in the game)
 

Trish was in the human world. she called Nero and asked him to help her extract Dante from the demon world because she thought Dante was trapped there. (Here you play a few missions as Nero who makes his way into the demon world after defeating some demons and opening a gate with Yamato.) The gate which Nero had activated was the other side of Sparda's gate in the underworld. when Nero entered the demon world, Vergil was still at the gate. The two fought over Yamato and Nero was about to lose it. Trish who arrived shortly after Nero saved him using her teleporting ability. she told Nero that their priority was finding Dante not wasting time with Vergil. Nero agreed with her and the two went after Dante.

Vergil didn't understand why Trish had his father's sword. Instead of following Trish and Nero, Vergil decided to meet them at the place where Mundus was sealed because he knew that's where Dante will be. When he reached that place, Vergil found out that he was too late and that the demon posseses the power of Mundus. Vergil attacked immediately and a battle started. Vergil wasn't able to end that battle alone then Dante arrived. when the new emperor realized that he was losing the battle, He teleported Dante to another dimension in order to ease his battle. Dante managed to seal him alone and returned back to the demon world. Vergil was surprised to see Dante defeat the most powerful demon without using the sword of Sparda. He realized that even by having Sparda he won't become the strongest demon because that won't make him stronger than Dante so he didn't even try to take his amulet or his father's sword or even Yamato. Vergil's new plan was to make his own power without using the power of Sparda or anyone else the same way Sparda made his. Dante, Trish and Nero returned to the human world while Vergil stayed in the demon world seeking more power.

The End
WOW... if you think reading all this is hard try writing it.
Hope you loved it

I've been playig RE5 recently. And although I'm a fan of the game since the days of PS1, I never played it before RE5. I used to just watch my brother play it and help him solve puzzles and find keys, however; I decided to play RE5 on my PC and it was a bit different from what I thought being based on killing only with no mystery or hard puzzles that make you lose your head till you find the way.

I expected to play a typical resident evil game but that is not what I found. It was different from earlier games like "code veronica" but I also loved the new changes and variety of gameplay especially the chapter select mode which gives you freedom during the game.