Maths mech question

Looks like youve badly drawn the vector addition. So the 3N will point north east and tip to tail the 5N will head south. The angle between them is theta. It looks like youve done the wrong diagonal of the parallelogram.
Note if you were in an exam and thought it was wrong, you could do the x and y coordinates seperately and then do pythagoras. The cos rule essientially does that and is more direct, if you do it properly.

I thought that's what I've drawn, I drew the 3N north east and the 5N south from the tip of 3N. Then the angle between them should be 180-theta surely?

Youve drawn tail to tail and the angle between them is indeed 180-theta. Vector addition is tip to tail. There are examples in textbooks/online just do a quick google, but youd move the 5N arrow and join its tail to the head of the 3N so the angle between them is now theta.

I've checked my diagram again and it seems to me that's what I've done. I'm referring to the triangle below, where i''ve applied cosine rule next to it but I've connected the tail of 5N to the tip of 3N?

In that diagram you have done that, but the angle between them now is theta.

but in the diagram above that I've drawn out, the angle between the vertical and 3N is theta so shouldn't the angle between 3N and 5N be 180-theta because it is a straight line?

Why not draw clearly the parallelogram which you think is relevant for the tip to tail vector addition and upload it. Obv the resultant will be one of hte diagonals.