If the first and second letters in the word 'LANGUAGE' were interchanged, also the third and the fourth letters, the fifth and the sixth letters and so on. Which letter would then be the fifth letter counting from the left?

Let's list the original letter sequence and index positions of the word LANGUAGE:
$$1:\text{L},2:\text{A},3:\text{N},4:\text{G},5:\text{U},6:\text{A},7:\text{G},8:\text{E}$$

Now, apply the pairwise interchange instructions:

* Interchanging 1st and 2nd letters ($\text{L}\leftrightarrow \text{A}$) $\to$ Position 1 becomes A, position 2 becomes L.
* Interchanging 3rd and 4th letters ($\text{N}\leftrightarrow \text{G}$) $\to$ Position 3 becomes G, position 4 becomes N.
* Interchanging 5th and 6th letters ($\text{U}\leftrightarrow \text{A}$) $\to$ Position 5 becomes A, position 6 becomes U.
* Interchanging 7th and 8th letters ($\text{G}\leftrightarrow \text{E}$) $\to$ Position 7 becomes E, position 8 becomes G.

The newly formed arrangement is:

$$\text{A L G N A U E G}$$

Counting from the left, the $5^{\text{th}}$ letter is A.