Below is an instruction that describes a task. Write a response that appropriately completes the request.

### Instruction:
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?

### Inputs:
table_name: table, columns: ['Administrative Panel', 'Agricultural Panel', 'Cultural and Educational Panel', 'Industrial and Commercial Panel', 'Labour Panel', 'National University of Ireland', 'University of Dublin', 'Nominated by the Taoiseach', 'Total']

### Response:
SELECT MAX Administrative Panel FROM table WHERE Nominated by the Taoiseach > 3 AND Agricultural Panel = 5 AND Cultural and Educational Panel > 2