To calculate the volume of co-trimoxazole injection 480mg in 5ml needed for a patient requiring 2040mg, we can set up a proportion:

480mg / 5ml = 2040mg / x

Cross-multiplying, we get:

480mg * x = 5ml * 2040mg

Simplifying:

480x = 10200

Dividing both sides by 480:

x = 21.25 ml

Therefore, you would need 21.25 ml of co-trimoxazole injection 480mg in 5ml for the patient requiring 2040mg.