The 1805 Large 5, Stems Half Cent is the second most common variety of the year, after the 1805 No Stems.
The nomenclature used for 1805 Half Cents can be confusing. The Small 5 is indeed small but The Large 5 is actually a normal-sized 5 relative to the other digits in the date, while the Small 5 is indeed small. Perhaps the easiest way to tell them apart is by comparing the distance of the 5 relative to the bust. On the "Large" 5, the tip of the 5 is close to the bust; on the Small 5, the 5 is well away from the bust.
Only a small number of Mint State 1805 Large 5, Stems Half Cents are known, most with little or no trace of original Mint Red. Red-Brown examples are exceedingly rare and nonw are known with full Mint Red.
Sources and/or recommended reading:
"American Half Cents, Second Edition" by Roger S. Cohen, Jr.