Five. (25 points) For any real numbers $x, y$, define the operation as follows: $x * y=a x+b y+c x y$, where $a, b, c$ are given numbers, and the right-hand side involves the usual addition and multiplication of numbers (for example, when $a=1, b=2$, $c=3$, then $1 * 3=1 \times 1+2 \times 3+3 \times 1 \times 3=16$). It is known that the defined operation satisfies the conditions: $1 * 2=3, 2 * 3=4$, and there is a non-zero number $d$ such that for any real number $x$ we have $x * d=x$. Try to find the values of $a, b, c, d$.


Given $x * d=a x+b d+c d x$, for all real numbers $x$, we have $a x+b d+c d x=x$, which means $(a+c d-1) x+b d=0$. Therefore, we have
$$
\left\{\begin{array}{l}
a+c d-1=0, \\
b d=0 .
\end{array}\right.
$$

Since $d \neq 0$, it follows that $b=0$. Thus, $x * y=a x+c x y$. From $1 * 2=3$ and $2 * 3=4$, we get
$\left\{\begin{array}{l}a+2 c=3, \\ 2 a+6 c=4 .\end{array}\right.$ Solving these, we find $a=5, c=-1$.
Then, from $a+c d-1=0$, we solve to get $d=4$.
Therefore, $a=5, b=0, c=-1, d=4$.