The reason behind you are getting null result once you are using CONVERT_TZ MySQL function is that TZ time zone table have not been setup.
You can check that time zone table is set up or not.
select * from mysql.time_zone;
If it's giving null values then you need:
insert time zone in MySql if you want to use CONVERT_TZ MySQL function to convert a date from UTC to America New_Yark time zone.
You can run below query without update time_zone table.
SELECT DATE_SUB( order_date, INTERVAL 5 HOUR ) as OrderDate
FROM TABLE_NAME
With date format:
SELECT DATE_FORMAT( DATE_SUB( order_date, INTERVAL 5 HOUR ) , '%Y-%m-%d %h.%i.%s %p' ) as OrderDate
FROM TABLE_NAME
Please have a look similar question.
MySQL CONVERT_TZ()
It will help you in "How to insert timezone in MySql".