, 2025

We begin by naming shapes shown by the thick lines 1, 2, 3, 4,
and 5, as shown in the diagram.

We also adopt the notation [row number, column number] to refer to
the contents of specific squares in the diagram.

For example, we are given that $[2,3]$ is $D$ (this is in shape 3), and $[2,4]$ is $A$ (this is in shape 2).

It is important to note that the solution that follows is one of many
different ways to arrive at the final answer.

Since $[3,2]$ is $C$, then $[2,1]$ cannot be $C$ (shape 1 already has $C$), and $[2,2]$ cannot be $C$ (column 2 already has $C$), and thus the $C$ in row 2 must be $[2,5]$.

Since row 5 already has an $E$, then
the $E$ in shape 5 cannot be in row
5, and thus $[4,2]$ is $E$.

Row 2 is missing $B$ and $E$ and since column 2 has an $E$, then $[2,1]$ is $E$ and $[2,2]$ is $B$.

The letters determined to this point are included in the diagram
below.

Since shape 2 already contains $A$
and row 1 is missing $A$, then $[1,1]$ is $A$.

Also, column 4 already contains $A$
and so $[5,4]$ is not $A$ which means that $[5,2]$ is $A$ (since shape 5 is missing $A$).

The letters determined to this point are included in the diagram
below.

Shape 1 must contain $D$ somewhere
in column 1 and so $[5,1]$ is not
$D$. Since shape 5 is missing $D$, then $[5,4]$ is $D$.

Shape 4 is missing $A$, $B$ and $D$. Since column 4 already contains $A$ and $D$, then $[3,4]$ cannot be $A$ or $D$, and thus $[3,4]$ is $B$.

Finally, shape 1 is missing $B$ and
$D$. Since row 3 contains $B$, then $[3,1]$ cannot be $B$, and so the letter in the shaded
square, $[4,1]$, is $B$ as shown.

The completed diagram is included below. Given the initial 5 letters
and their locations, there is exactly one way to complete this
diagram.