Finding conditional probabilities in a Markov chain

Question

I am working on a Markov chain problem and need help understanding how to find the vector of probabilities for the third step, given that we have ended up in state 2 or 5 at the fifth step. Here is the transition matrix I am m working with: $$ P = \left[ \begin{array}{ccccc} 0 & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ 0 & 1 & 0 & 0 & 0 \\ \frac{1}{4} & \frac{1}{4} & \frac{1}{3} & 0 & \frac{1}{4} \\ 0 & 0 & \frac{1}{2} & 0 & \frac{1}{2} \\ 0 & 0 & 0 & 0 & 1 \end{array}\right] $$ We start in the state (1, 0, 0, 0, 0), which corresponds to the first column of the matrix. Can someone guide me through the steps of solving this problem? I have considered using a straight approach (just look at the graph and possible states), but I feel like there is a general approach (because the matrix can be more complicated than in this task). Any help or suggestions would be greatly appreciated!