Algebra

We can note something really important to solve this problem. 

First off, let's note that

$(x+y)^3 = x^{3}+3x^{2}y+3xy^{2}+y^{3}$

Plugging in all the information we already have from the problem, we get that

$8=5+6xy\\ xy=1/2$

The reason we need the value of xy will come into play later. 

Now, let's also note that

$(x+y)^2 = x^2+2xy+y^2$

Isolating x^2+y^2, we get that

$x^2+y^2 = (x+y)^2 - 2xy$

We already know all the terms of the equation we needed to find x^2 + y^2. 

Plugging in 1/2 and 2, we get

$x^2 + y^2 = 4 - 1 = 3$

So our answer is 3. 

Thanks! :)