mysql string to date
Use %H instead of %h.

select STR_TO_DATE('03.05.2010 00:00','%d.%m.%Y %H:%i');


Or, if HH:MM are always 00:00 you can use date part only:

select STR_TO_DATE('03.05.2010 00:00','%d.%m.%Y');


Check it here: http://rextester.com/CCPKR29919

As @a_vlad has pointed out on his comments, %H is used to format hours as 00..23 and %h as 01..12.

Have a look at DATE_FORMAT() on MySql docs.