Answer: 15 buds on the tree branch.
Explanation:
After 5 days, the number of buds on the tree branch can be calculated by adding the initial number of buds to the number of buds that sprout each day.
The initial number of buds is 5.
Each day, 2 more buds sprout.
So, after 1 day, there will be 5 + 2 = 7 buds on the tree branch.
After 2 days, there will be 7 + 2 = 9 buds on the tree branch.
After 3 days, there will be 9 + 2 = 11 buds on the tree branch.
After 4 days, there will be 11 + 2 = 13 buds on the tree branch.
Finally, after 5 days, there will be 13 + 2 = 15 buds on the tree branch.
Therefore, after 5 days, there will be 15 buds on the tree branch.