Group df by animal and keep only the rows belonging to groups whose total visits exceeds 5, dropping every row from groups that don't meet this condition. Return the filtered DataFrame with its original columns and index.

Sample data: df:

  animal  age  visits priority
a    cat  2.5       1      yes
b    cat  3.0       3      yes
c  snake  0.5       2       no
d    dog  NaN       3      yes
e    dog  5.0       2       no
f    cat  2.0       3       no
... (10 rows total)