Selecting multiple attributes, greater and less than

I think you need to use the following instead:

"GRIDCODE" >= 10 AND "GRIDCODE" < 15

You need to switch the => operators and specify again the attribute field for the second term (i.e. < 15).

You can also use:

"GRIDCODE" IN ('10', '11', '12', '13', '14')

If the data type for the field is String rather than a numeric type. Otherwise use the method described by Joseph.