How many Thursdays are there in February 2024, given that the month begins on a Thursday and 2024 is a leap year?

1. Determine the total days in the month:
Since 2024 is a leap year, February has $29\text{ days}$.

2. Map the Thursdays:
The month begins on a Thursday, which means February $1^{\text{st}}$ is a Thursday.
The subsequent Thursdays occur at intervals of $7\text{ days}$:

* $1^{\text{st}}$ Thursday: February 1
* $2^{\text{nd}}$ Thursday: $1+7=\text{February 8}$
* $3^{\text{rd}}$ Thursday: $8+7=\text{February 15}$
* $4^{\text{th}}$ Thursday: $15+7=\text{February 22}$
* $5^{\text{th}}$ Thursday: $22+7=\text{February 29}$

Since February 29 is within the month, there are exactly $5$ Thursdays.