1. Identify which series has lines counted from the red end

In the hydrogen spectrum:

• Lyman series: transitions ending at $n=1$ (ultraviolet)
• Balmer series: transitions ending at $n=2$ (visible region)
• Paschen series: transitions ending at $n=3$

Since the question says "from the red end", it refers to the Balmer series in the visible region, where the first line is the longest wavelength (reddest).

2. Write the Balmer transitions in order

For Balmer series, electron jumps are: $n \to 2 \quad (n=3,4,5,\dots)$

Thus the first few lines are:

• First line: $3 \to 2$
• Second line: $4 \to 2$
• Third line: $5 \to 2$

As wavelength decreases, the color shifts away from red.

3. Match with the given options

Options:

• A: $5 \to 2$
• B: $4 \to 1$
• C: $2 \to 5$
• D: $3 \to 2$

The third line from the red end is: $5 \to 2$

So the correct option is A.

4. Check other options

• B: $4 \to 1$ belongs to Lyman series, not Balmer.
• C: $2 \to 5$ is an absorption transition, not an emission line in the series.
• D: $3 \to 2$ is the first Balmer line, not the third.

Therefore, the correct answer is: $\boxed{5 \to 2}$