The example above is for tires manufactured after 2000:
DOTU2LLLMLR5107 = MANUFACTURED 51 WK OF 2007
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The example below is for tires manufactured before 2000:
DOT EJ8J DFM 408 = MANUFACTURED 40TH MONTH OF THE 8TH YEAR OF THE DECADE
As a general rule, you do not want to use a tire more then 6 years old. That is not written anywhere but a general consensus among tire experts and engineers.
PS: The above pictures were taken from tire rack and you can find some really good information there.
Manufactured during the 51st week of the year