A celery cultivar, designated ADS-5, is disclosed. The invention relates to the seeds of celery cultivar ADS-5, to the plants of celery line ADS-5 and to methods for producing a celery plant by crossing the cultivar ADS-5 with itself or another celery line. The invention further relates to methods for producing a celery plant containing in its genetic material one or more transgenes and to the transgenic plants produced by that method and to methods for producing other celery lines derived from the cultivar ADS-5.