Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE table_name_37 (administrative_panel INTEGER, cultural_and_educational_panel VARCHAR, nominated_by_the_taoiseach VARCHAR, agricultural_panel VARCHAR)

### Question ###
What is the biggest administrative panel with a nominated by the Taoiseach greater than 3 and an argricultural panel of 5, plust a cultural and educational panel larger than 2?

### Accurate SQL ###

SELECT MAX(administrative_panel) FROM table_name_37 WHERE nominated_by_the_taoiseach > 3 AND agricultural_panel = 5 AND cultural_and_educational_panel > 2