Someone already posted the correct reason. The number 4 in Japanese is "shi" which is also the word for "death."

It's similar to the sort of superstition attached to the number 13 in the West. 

There's no hate for the number 4, it's just considered bad luck. 

So, apparently, the number four is worse than I thought it was in Japan. It's so powerful that in some buildings, there is no fourth floor, it just goes from third to fifth. I don't see why Sony can't just call it the Playstation 5.

Or the Playstation 3S.

They will copy apple, The New PlayStation.

srry it was a bad joke. 

They should call it the PlayStation 6. Why go one step beyond when you can just leave the competition in the dust?

Paystation Ultra PSU

Playstation Xtreme PSX

Or they could go the iPad route and go back to plain old Sony PlayStation, or thatther The New Sony PlayStation.

I would prefer them to keep it as Playstation 4/PS4.
If they gave the console a new name, that would be okay i guess. But skipping 4 and going straight to 5 seems really dumb.

The Japanese word for four, "shi" also means death. The Japanese also use the word "yon" for the number four.
Nintendo Ultra later called Nintendo 64 was indeed the fourth Nintendo system. Japanese rarely use the number four in naming products due to the reference death.

Play Station 4 or PS4 would not be a popular name for the next Playstation in both Japan. Play Station 4 or PS4 name would be highly controversial and culturally insensitive to the Japanese. 

Instead of just using a generic number for a console system,  Sony may have to add a creative/emotive word to the Play Station and make it marketable for Play Station fans all over the globe, especially in Japan. 

Include PS Move 2 with both dildo and hands-free depth detection capable camera and call it PlayStation TE (Total Experience).