Answer:
The answer is A - I'll explain why below :)
Step-by-step explanation:
So, to start - Byzantine Empire was created after the Roman Empire was split into two parts, Western and Eastern. BE was the Eastern part. It existed from from 4th century; it was able to maintain most of it's territories throughout the first centuries of it's existence, but later continuously losed them over time. It's existence was ended in 1453, when it's capital Constatinopole (modern day istanbul) was taken by the Ottoman Empire (it's modern equivalent being Turkey). For the purpose of the question - we should assume that the BE was thriving around 4th-6th century.
So, how does that timeline relate to our answers?
A. The dark ages - this is correct! The western part of the Roman Empire fell in 476, but by that time - it has already been in decline for a long time. That period, and several following centuries, were marked by fragmentation, technological and cultural regression, and wars for power - hence the name.
B. Rome and the rest of Europe was also thriving - not quite! As I've explained before, the period we're looking at was definitely not great for the rest of Europe.
C. The age of exploration - Nope. The age of exploration is a term referring to a period of European discoveries in 15-17th Century.
D. The renaissance - This one refers to a cultural period in Europe in 15-16th century, so clearly no overlap with the BE's good times (and little if any with it's existence altogether).