Help preparing for MySQL Master Slave Replication
Common question, common answer.  The first time you set it up it is painful.  But, if you do it one of several 'right' ways, the subsequent backups will be less painful.

LVM -- requires OS involvement.  But backup takes about 1 minute, regardless of data size.

Replication -- requires a full copy.  Xtrabackup can do it relatively painless for InnoDB, but blocks for MyISAM.  Corollary:  You should move away from MyISAM.

Disk sync (via rsync or whatever) -- takes long for 400GB, but it is clean.  You must shutdown MySQL during the operation.  (LVM would make it short.)

If you have an adequate backup, and can build a Slave from it, then that may be your best bet.  In the future, take backups from the Slave.  (Even better, clone one Slave from anothor.)

Yes, once a Slave exists, pt-table-checksums and pt-table-sync are a good idea.

Also, you need to move from 5.5 to 5.6 to 5.7.  It won't be long before 5.5 is no longer supported.