A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters. From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.

The player initially has two plates containing the letters A and D.

Let us analyze the additional plates provided in option (B):

1. The first plate is the letter R.

2. The second plate is an inverted A (i.e. $\forall$). Rotating it by $180^\circ$ in its plane gives the letter A.

3. The third plate is an inverted R. Rotating it by $180^\circ$ in its plane gives the letter R.

Combining the initial two plates $(\text{A}, \text{D})$ with the three rotated plates from option (B) $(\text{R}, \text{A}, \text{R})$, the available letters are:

Arranging these five letters forms the word:

Since RADAR reads identically forwards and backwards, it is a valid five-letter palindrome.

Therefore, option (B) is the correct choice.