No, it often does absolve you. The theory is that the request to produce is utilizing the subpoenaed person's knowledge to identify sources of incriminating information and hence, the act of production, separate and apart from the contents of the documents, is an act of self-incrimination.
In order for 5A not to be available, the requests have to be very specific, like "produce your tax returns from 2015" would be OK, but "produce any and all documents constituting, referring to or related to your business dealings in Russia" would not. In the second example, the act of production implies an admission that the person has business dealings in Russia, which in a given case, could be incriminating, while in the first example, nothing is implied by the act of production other than the fact that a tax return for the specified year exists.
If that all seems convoluted, the short answer is this: sometimes it does, and sometimes it doesn't.