In 1006, the entire Christian world would have been using the Julian calendar (Gregorian isn't invented until 1582), although there is some variance on when different countries recognized the new year in the Julian calendar. Albeit, May is one of those months where everyone agreed on the year.
Outside of the Christian world, the correlations between different calendars and the Julian calendar is quite well-known, because by the time Europeans contacted people following those calendars, they can ask "what day is today" and get the Gregorian-Julian-local calendar correspondence. If you've got a stable year count (not based on reigning kings), it's easy to work out older dates. If you have regnal year numbering, and you have enough written evidence that you can decisively determine how long each king reigns for, then you can also carry that over to a complete calendrical determination.
In cases where the calendar is no longer used, you can match up calendars by looking for records corresponding to known (largely astronomical) phenomena (eclipses are particularly helpful) and get correlates that way. This is how we match the Mesoamerican Long Count to the Julian/Gregorian calendar.
Outside of the Christian world, the correlations between different calendars and the Julian calendar is quite well-known, because by the time Europeans contacted people following those calendars, they can ask "what day is today" and get the Gregorian-Julian-local calendar correspondence. If you've got a stable year count (not based on reigning kings), it's easy to work out older dates. If you have regnal year numbering, and you have enough written evidence that you can decisively determine how long each king reigns for, then you can also carry that over to a complete calendrical determination.
In cases where the calendar is no longer used, you can match up calendars by looking for records corresponding to known (largely astronomical) phenomena (eclipses are particularly helpful) and get correlates that way. This is how we match the Mesoamerican Long Count to the Julian/Gregorian calendar.