Ron Guth: Actually, there were two different 1805/4 overdated dies, both of which have 4's clearly visible beneath the 5, even to the naked eye. Apparently, dies were prepared in 1804 for an anticipated coinage of half dollars which never materialized. Thus, in 1805, the engravers took the two leftover 1804 dies and punched a 5 over the 4.
All of the 1805/4 Half Dollars are scarce and at least one of the die varieties (O-103) is rare (and its die states are even rarer still).
Based on the PCGS Population Report, the 1805/4 overdated half dollar is approximately two to three times as rare as the normal 1805 half dollar. Mint State examples of both types are exceedingly rare and the finest examples certified by PCGS thus far (as of May 2011) are a pair of MS65 examples.
Louis E. Eliasberg, Sr. Collection - Bowers & Merena 4/1997:1681, $82,500 - Heritage 8/1998:6598, $103,500 - D. Brent Pogue Collection - Stack’s/Bowers & Sotheby’s 5/2015:1109, $111,625