The question makes you reflects on the meaning of the transform matrix (which construction process w.r.t. DH parameter is given).
A transformation matrix denotes the transformation from one frame to the next, by mean of both a rotation matrix ($R$) of the second frame w.r.t the first frame expressed in the first frame, and a position vector ($p$) of the second frame origin expressed in the first frame.
The transformation matrix is constructed as follows:
$T=\begin{bmatrix} R & p \\ 0~0~0 & 1 \end{bmatrix}$
Thenn what I would do, although it is bit unclear from the formulation, I would suspect that the information given relative to the distance between link 2 and 5 (is 5 the end effector?) are given in the base frame (0), otherwise the information relative to $^2_5T$ are not useful.
From there using the transformation matrix at hand and considering the suggested vector you get a system of equations.
That gives you relationships between all the mentioned quantities, but there I am blocked by the information concerning the the $y$ component of the position of end-effector w.r.t 2 expressed in 0, as it didn't match my result and left me with $d_5$ unknown (same if I make the assumption that the information about the vector are expressed in 2). Although if the vector component information concerns $x$ than it is possible to get a numerical evaluation of $d_3$.
NOTE: done during my coffee break