I finally got it to work, but it seems like it was a roundabout way. I created a view from the query I posted and then ran the subquery:

SELECT DOCTOR_ID
FROM REFCOUNT
GROUP BY DOCTOR_ID
HAVING COUNT(DOCTOR_ID) >5

The relevant columns from the tables are:

DR
name (varchar(67), null)
doctor_id (PK,int, not null)

PT_ADMIT
admit_date (datetime, null)
referral_id (FK, int, null)

Thanks for your help!