The last five Mughal rulers in chronological order are as follows:

I. Ahmad Shah
II. Alamgir II
III. Shah Alam II
IV. Akbar II
V. Bahadur Shah II

Now let's go through each ruler and arrange them chronologically.

I. Ahmad Shah:
Ahmad Shah was the son of Jahandar Shah and became the Mughal emperor in 1748. However, his reign was short-lived as he was assassinated in 1754.

II. Alamgir II:
Alamgir II, also known as Ali Gauhar, succeeded Ahmad Shah as the Mughal emperor in 1754. He faced several challenges during his reign, including the invasion of Nadir Shah and the rise of regional powers. Alamgir II was assassinated in 1759.

III. Shah Alam II:
Shah Alam II, also known as Ali Gauhar, came to power after Alamgir II's assassination in 1759. He faced multiple invasions and was captured by the British during the Battle of Buxar in 1764. Shah Alam II was made a puppet ruler and had limited authority over the Mughal Empire. He died in 1806.

IV. Akbar II:
Akbar II, originally named Mirza Akbar, was the son of Shah Alam II. He became the Mughal emperor in 1806 after his father's death. During his reign, the British East India Company had gained significant control over India. Akbar II played a limited role as a figurehead ruler. He died in 1837.

V. Bahadur Shah II:
Bahadur Shah II, also known as Zafar, was the last Mughal emperor and the successor of Akbar II. He ascended to the throne in 1837 and his reign witnessed the events leading up to the Indian Rebellion of 1857. After the rebellion was suppressed, Bahadur Shah II was exiled to Rangoon, where he died in 1862.

In conclusion, the correct chronological order of the last five Mughal rulers is:
I. Ahmad Shah
II. Alamgir II
III. Shah Alam II
IV. Akbar II
V. Bahadur Shah II

So the correct answer is option 'A' - I, II, III, IV, V.