Can my husband sponsor my green card if he has filed the petition for his ex-wife in 2005?

There is no prohibition against a U.S. petitioner sponsoring a spouse, later becoming divorced and marrying another foreign national, and then sponsoring the second spouse. A heightened level of scrutiny can be expected, however, by immigration officials who may suspect marriage fraud. That heightened level of scrutiny may apply both to the new application, and to evidence that the U.S. citizen lived in a bona fide marriage with the first spouse too. Documentation of the bona fide nature of the first marriage already would have been supplied to the USCIS in connection with the first application, and generally is not needed in connection with an application for a second spouse except when the USCIS may have substantial reason to suspect fraud (for example, in an instance where the couple became divorced extremely soon after the foreign national spouse received her "Green Card"). One may find information and documents about a previously filed case through filing an application under the Freedom of Information Act. Note, however, that this process can take quite a long time, and it may be worthwhile to try additional efforts to identify the immigration attorney who handled the application process for the first spouse - that might include, for example, reviewing decade-old emails, credit card and checking records. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

Yes, he can file for you.