Yesterday I have 4 Shipyards. then I try to buy another one and I did it. so I was going to but aircraft carrier. after buying it I try to buy 5 aircraft to have 90 aircraft but i dont know why i cant do that. Do you know why? maybe This is bug in the game.

You probably lost Construction. I cannot check, but check your nation for that.

No, he has contruction. I think the problem is 85 is the max aircraft he can have, not 90 as he thinks. Base limit for aircraft is 50. Construction raises this by 10 to 60. A max of 5 carriers can provide aircraft at 5 per allowing you 25 additional aircraft for a total of 85.

If you don't have it already get FAB wonder

after I have FAB how many aircraft can i have?

if you also have construction and the 5 carriers you could have up to 105

Another question:
what's usage of 6th shipyard?

The maximum number of shipyards you can have is 5 (you currently have 4).