U.S. Code, Chapter 1, Title 4, Sec. 6 allows for a 24 hour flag display when a patriotic effect is desired, provided the flag is illuminated after dark.
24/7 By Presidential Proclamations and Public Laws
Presidential proclamations and laws authorize the display of the flag 24 hours a day at the following places:
Fort McHenry National Monument and Historic Shrine
Baltimore, Maryland (Presidential Proclamation No.2795, July 2, 1948)
Flag House Square (Mary Pickersgill's "Star Spangled" House)
Baltimore Maryland (Public Law 83-319, approved March 26, 1954)
United States Marine Corp Memorial (Iwo Jima)
Arlington, Virginia (Presidential Proclamation No.3418, June 12, 1961)
On the Green of the Town of Lexington
Massachusetts (Public Law 89-335, approved November 8, 1965)
The White House
Washington, DC. (Presidential Proclamation No.4000, September 4. 1970)
Washington Monument
Washington, DC. (Presidential Proclamation No.4064, July 6,1971, effective July 4, 1971)
United States Customs Ports of Entry
which are continually open (Presidential Proclamation No.4131, May 5, 1972)
Grounds of the National Memorial Arch in Valley Forge State Park
Valley Forge, Pennsylvania (Public Law 94-53, approved July 4, 1975)
There are dozens of sites that claim their specific locations and others are "officially authorized" by congress or the president. Often these are reported without any real documentary evidence found that this information is correct. Occasionally, we have to revisit an issue to assure we are accurate. Phil Nelson, 22 June 1998
Here are a few of the locations stated to have 24 hour flag displays. If you know of a presidential order, public law... prescribing this, then please inform the editor or the director.
The Betsy Ross House, Philadelphia, Pennsylvania
U.S. Capitol, Washington, D.C. pueble.gsa.gov explains
the Capitol practice (customary since WWI; the Capitol display could not be by executive order or proclamation,
because E.O.'s by definition don't apply to the legislative branch). Joe McMillan, 15 November 2002
Jenny Wade House, Gettysburg, Pennsylvania
Only civilian killed in the Battle of Gettysburg - doesn't she seem *really* obscure to merit specific Congressional or Presidential attention equivalent to these other places? Joe McMillan, 15 November 2002
Francis Scott Key's grave - a Frederick city site says the 15-star flag has flown at Key's grave day and night since 1949, which is after the U.S. Code was formulated, so if there is specific statutory authority, it should be easy to find. I couldn't. Joe McMillan, 15 November 2002
Arlington National Cemetery, Arlington, Virginia
not flown 24/7 from either flagpole on the cemetery grounds. Evidence: personal observation. The USMC Memorial, of course, is adjacent to the cemetery. Joe McMillan, 15 November 2002
U.S.S. Arizona Memorial, Pearl Harbor, Hawaii
not flown 24/7. navy website shows photos of morning
colors at the Arizona Memorial, which would be superfluous if the ensign flew 24/7. In fact, "On 7 March 1950, Admiral Arthur W. Radford, Commander in Chief of the Pacific Fleet at that time, instituted the raising of colors over Arizona's remains," according to website. That sounds to me as if the regular raising and lowering of the flag has a symbolism that would be defeated by leaving the flag up at all times. Joe McMillan, 15 November 2002
As stated about a year ago, by custom (not law) the U.S. Flag flies 24 hours a day in Taos, New Mexico and has since 1861 when Kit Carson rode into town, climbed up the flag pole, nailed a U.S. Flag at the top and dared any pro-Confederates to try and lower it! Dave Martucci, 20 June 1998
This sounds like one of those trick trivia questions, so I wouldn't be surprised if whoever posed it thought there were only five flags on the moon. I don't see why the fact that they are not lowered at "night" would affect the fact that they also are not half-masted.
Another trick answer would be "on the back of U.S. currency." There's one U.S. flag on the back of the $10 bill, two on the back of the $20 bill, one (I assume) on the back of the $50 bill, which depicts the U.S. Capitol. Those four plus one on the moon would be five.
The Iwo Jima memorial is not a correct answer. It is half-masted, although I believe that is a relatively recent practice and certainly looks odd when it is done.
As for the UN, wouldn't the U.S. flag be half-masted there along with all others for, let's say, the death of a Secretary General? If not, then the same half-masting rules would also apply at other UN offices in Geneva, Rome, Vienna, etc., which might yield five locations.