Two poles are 2m apart. A wire links them together at the top. If the poles are 2.8m and 5m in height, how long is the wire?

Well, technically the wire will not form a straight line but a catenary so it will be slightly longer than what the others have calculated, depending on the tension it's under.

But I suppose that you are not asked for that but an idealized scenario where the wire stretches along a straight line. In which case the answer is √(221)/5 m ≈ 2.97 m.

The others have given you the obvious answer but I must ask " how did you get the wire in place"?

If you tried to thread the wire you would need to attach it to the top of the 2.8 m pole.

Go down the pole to the base of the other pole. Then climb it to the top to attach the wire.

So at some point the wire needs to be long enough to get from the top of the 2.8 m pole to the base of the other pole.

Otherwise I don't know how you got the wire into position. ie 3.44 m of wire is needed to do the job.

Always, always draw a diagram

wire is hypotenuse of a triangle 2 by 2.2

Add the squares of these = 4 + 4.84

take square root of 8.84

wire is 2.97m long

Using Pythagoras' theorem it is 2.973213749 or about 3m in length

If the wire is tight, its length is

sqrt(2^2 + 2.2^2)

= sqrt(8.84) = 2.97 m.