The stardate is a very complicated thing to understand. The 5 at the beginning simply represents what century we are in currently in reality. If there is a 4 at it would represent the 1900s. The 5 states that the stardate in question would tell that the century is 2000s.
The second number represents the year. So the 02 represents 2002. If it was 74, it would represent two possible things. If the number at the front is a 4, it would represent 1974. If it was a 5, like above, it would be 2074.
The third number, the 19, represents the day. The 3rd day of the month would be represented with a 03. So the day in question is the 19th of some month.
The last number, following the decimal, or "point" as referred in the Star Trek Series, is the month. 1 through 12. Simply, the three stands of March.
So in closing, the date above is decoded like this:
5 = 2000s
02 = 2002
19 = 19th Day of the Month
.3 = March
March 19th, 2002