Solution:

It is important to note that

Distance = Speed × Time.

1. The snake has entered the hole when its tail just comes into the hole. It is given that 13 seconds elapse from the time the snake's head enters the hole till its tail enters. Thus,

Length of the snake = Distance traveled in 13 seconds
= (5 cm/s) × (13 s) = 65 centimeters.

2. The snake has exited the hole when its tail just leaves the hole. The distance traveled from the time the snake's tail just enters the hole till its tail just leaves the hole equals the length of the hole. Thus,

Time for the snake to exit the hole after entering it =
Length of the hole / Speed = (6.2 m) / (5 cm/s) = (620 cm) / (5 cm/s) = 124 seconds.

Food for thought:

Are there any inaccuracies in the answers above? Does it matter that the bodies of snakes are usually wavy and not straight when they move?