The uncredited Date a Live V opening version is now available on Kadokawa Animation's official YouTube channel. You can watch the video below:

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Date a Live V Open Sequence (Paradoxes)

The name of the song is “Paradoxes”, by Miyu Tomita. The ending theme song titled “Hitohira” by Sweet ARMS was also previously released:

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V Ending Sequence (Hitohira) live stream date

Date a Live V premieres on April 10, 2024 and currently has 3 episodes. Jun Nakagawa is directing it at studio GEEKTOYS. The same staff also made a fourth season in 2022. Keitaro Motonaga directed the first season at AIC+ in 2013, the second season at Production IMS in 2014, and the fourth season at JC Staff in 2019 You can watch season 5 on Muse Asia and Crunchyroll. Muse Asia describes the plot of the current season as follows:

The spirits have the appearance of human girls, but they are different from humans.
They are even called enemies of humanity because of their powerful ability to cause disasters known as “space earthquakes” when they appear from another dimension.
The only means humanity has to deal with the threat of these Spirits is to destroy them by military force, or…
Dating and dating them they could not succumb to the power of love!
Shido Itsuka has the ability to seal a Spirit's power by making her fall in love with him and kiss her.
He saved humanity and the Spirits with his power, but an upheaval was about to happen to him.
DEM Industry, one of the world's largest corporations specializing in Realizers, is searching for the power of the Spirits and attacks with all its might to take Shido's life.
Then, a mysterious girl from deep in Shido's memories appeared.
The biggest battle in history, with so many intertwined agendas, will begin.

The anime is based on the novel series Date a Live by Koshi Tachibana. Fujimi Shobo published it with illustrations by Tsunako from 2011 to 2020 and had a total of 22 volumes in circulation. Yen Press is publishing this novel series in English.

Source: Official KADOKAWA YouTube
© Koshi Tachibana, Tsunako/KADOKAWA/“A Live V Production Committee Day”