The author (Ichiei Ishibumi) tweeted on his official twitter that if the Oversea fans want more animated seasons, they need to buy the official english light novels.
So it is actually a greenlight for Season 5, so grab your money and credit cards and support DxD by buying High School DxD, Vol. 1 (light novel): Diablos of the Old School Building.

https://twitter.com/ishibumi_ddd/status/1318893022931607553