Well, I suppose the most important piece of information this question is giving you is that DEF=PQR
We know from letter correspondence that DE=PQ and since PQ=5, DE=5
Now we can use the pythagorean theorem to finish it off becase we know DF and DE and we are solving for EF
Thus we get DF^2=DE^2+EF^2 so 13^2=5^2+EF^2
Thus 169=25+EF^2 so EF^2=144. Therefore, EF=12
