I'd say it is acceptable however in the U.S., we most commonly use 04/2005 or April 2005.

Hello Angela: "Is it acceptable to write April 2005 as 2005/04?"----Angela It is awkard. Common conventions are: April 11, 2005 or 04/11/2005. Or, one can write April Eleventh 2005 as April 11th, 2005. Then just because of my military training, you find uncommon datings as the one I employ, which is like this: 11 April 2005 ---Warm Regards, Bruce

In writing it is not acceptable under any circumstance. Do so and you will lose points!

It's passable, but it's hard to imagine a reason to justify it.