What is the age difference between Frasier and Niles?

Most Internet sources (Wikipedia, Wikia, IMDb, etc.) state/estimate that Frasier was born in 1952 while Niles was born in 1957. There appears to be no listed source for Niles' date of birth, but Frasier is well covered:

The details of Frasier's birth are erratic and changing.

• In Cheers episode "It's a Wonderful Wife", the bar celebrates Frasier's birthday in late February.
• In one episode, it is established he was born in March 1952.
• In the episode "Back Talk" it is revealed that Frasier's birthday is the day after one of Queen Elizabeth's children. As Prince Edward, Earl of Wessex (born March 10, 1964) is the only one of Queen Elizabeth's children born in March, Frasier's birthday would be March 11, 1952. However, the episode "The Fight Before Christmas" takes place a few days after "Back Talk" (according to the storyline) which contradicts a March birthday. Also, this date is established by Daphne reading a newspaper from the day Frasier was born and assuming it was a current newspaper. This would suggest Frasier was born in 1964, but he is clearly older than this (mentioning being in his 40s consistently before this). Other children of Queen Elizabeth include Anne, Princess Royal (born August 15, 1950) and Prince Andrew, Duke of York (born February 19, 1960). Charles, Prince of Wales was born November 14, 1948, but this was before Elizabeth ascended the throne. If Frasier was born prior to 1952, then the "Queen Elizabeth" referred to in the paper could be Elizabeth Bowes-Lyon, wife of King George VI and the queen-mother of Elizabeth II (although her last child was born in 1930). Alternatively, a third "Queen Elizabeth" might have been intended, or the joke from "Back Talk" was simply historically inaccurate.
• In the episode "The Late Dr. Crane" a local Seattle news station incorrectly reports that Frasier died of a heart attack. Frasier's picture is shown on the screen with the dates 1952-1999.
• In the episode "Are You Being Served?" it is revealed that he was named after one of his mother's lab rats. In the same episode, a second birthday contradiction appears: His mother's journal indicates that as of April, she was pregnant with Frasier, making a March birthday impossible. Frasier has one younger brother, Niles (David Hyde Pierce), who, like Frasier, was also named after one of his deceased mother's lab rats.
• The episode "Party, Party" suggests a May birthday.
• In a trailer made for the British television network Channel Four, Frasier says that he was born on the 4th day of the 4th month.