MySQL has good date arithmetic.  For example, the expression
 CURDATE() + INTERVAL 30 DAY
gives a datetime value denoting midnight 30 days hence.  Similarly 
CURDATE()  + INTERVAL 61 DAY 
yields midnight on the 61st day.
So a query of the form
   SELECT ID
     FROM APPROVAL
    WHERE Level = 5
      AND `DateTime` >=  CURDATE() + INTERVAL 30 DAY
      AND `DateTime` <   CURDATE() + INTERVAL 61 DAY
will yield what you want. Notice the use of >= for the beginning of the range of days, and the use of < and an extra day for the end of the range. We do that because we want all items from the 60th day, and none from the 61st day.
A compound index on (Level, DateTime) will make this query very efficient to satisfy.  
Notice that an expression like
    DATE(`DateTime`) <=   CURDATE() + INTERVAL 60 DAY  /* slow! */
will also yield correct results, but the presence of the the DATE() function call on the column to be searched makes it unsargeable. That is, it makes MySQL unable to use an index to satisfy the search.