One of the rare "modern" U.S. stamps, the red-brown and black $5 Coolidge can present problems for collectors. The normal stamp is carmine and black. The difference in color, according to an analysis done at the Bureau of Engraving and Printing, was due to a contaminant, possibly a black pigment or carbon black. 

The original discovery is credited to George Sloane, the noted American philatelist. Mr. Sloane sent a block of eight to the Bureau asking for clarification as to how the color variety came about. Along with a disclaimer from the Bureau advising that "we neither wish nor attempt to influence philatelic considerations" came a note that through examination of "spectrophotometric curves" it was apparent that Sloane's stamps were indeed color varieties as the result of ink composition at the time of printing, rather than as a result of subsequent environmental factors. 

This is an important distinction and collectors should take this to heart before shelling out for an uncertified copy of 834a. The problem is this: stamps can be induced to change color through various environmental factors. Exposing your stamps to sunlight is one example. In the case of the $5 carmine and black stamp, exposure to sulfur dioxide under the right conditions can result in a stamp that is very difficult to distinguish from the true red-brown and black error stamp. The stamp must be submitted for spectral analysis to verify that it is an ink variety and not a color changeling. 

That is not to say that there might not be a few of these waiting for an astute collector to find. An article in the 1990 U.S. Specialist noted that there were at least nine plate blocks of this error known, most of them expertized and illustrated. Roland Rustad, author of the seminal work "The Prexies" notes that twelve plate blocks are now known. Since there is only one plate block available from each pane of 100 stamps, there would be a possibility that as many as 1200 of these stamps were in the hands of the public at one time or another and possibly many more. Ralph Davis, a respected philatelist and long-time postal employee of the era, noted that the Post Office was aware of this "error" and that it was reported to the Bureau at the time. According to Davis more than two-hundred thousand of these color errors, which the Bureau considered "inferior" printings, were either pulled or recalled and ultimately destroyed. 

Of the at least twelve panes that most likely reached the public's hands, it is certain that the number saved by collectors was much smaller, since $5 was a lot of money in 1938-1939 (the date when these stamps were most likely produced), and the stamps that were saved were more likely than not to be in the form of position pieces and/or plate blocks. Still, at least two used singles have been certified and the possibility that more of these are waiting to be found is a distinct possibility. Many of the unused singles known today are from blocks broken apart to obtain choice singles, a shame since the blocks were a piece of philatelic history, but understandable since the financial reward of a graded superb single is so great. 

A "Power Search" for "834a" on the Siegel website will yield an interesting array of colors for the stamp. Keep in mind that the spectral analysis of the stamp by the Bureau itself suggests that the "red-brown" ink, which the Bureau referred to as "madder brown", had black impurities. I would suggest using the reddish-brown or darker examples for comparison. 

Good luck hunting, but remember, don't be fooled by the sulfurreted changelings which can look an awful lot like the real thing. A scan could not possibly reveal if a stamp were environmentally altered, so beware.

References:
1951 Scott Specialized Catalogue of U.S. Stamps
Roland Rustad The Prexies - 1994 - published by the Bureau Issues Association
Sloane's Column p.79
The U.S. Specialist Vol. 51 No.4 April 1970 pp. 152-153
The U.S. Specialist Vol. 61 No.7 July 1990 pp. 399-410
R. H. White - Color in Philately (1979) - Spectrophotometry for the Analysis and Description of Color

Note: I must apologize for the lack of an example, but I do not have access to a photograph or scan of the error stamp to place on this page..