Explanation:

To understand why the maximum number of newly created nodes in the process is 5, let's first understand the structure of a B-tree and how it works.

- A B-tree is a self-balancing search tree data structure that maintains sorted data and allows efficient insertion, deletion, and search operations.
- It is commonly used as an index structure for large database tables.
- In a B-tree, each node can have multiple keys and child pointers.
- The number of keys in a node is always one less than the number of child pointers.
- The keys in a node are sorted in ascending order.

Structure of a B-tree:

- A B-tree has multiple levels, starting from the root node at the top and leaf nodes at the bottom.
- Each level of the B-tree except the leaf level must have at least ⌈m/2⌉ keys, where m is the maximum number of keys a node can hold.
- The root node can have a minimum of 1 key, and the leaf nodes can have a minimum of 0 keys.

Insertion in a B-tree:

When a new key is inserted in a B-tree index, the following steps are followed:

1. Start from the root node and compare the key to be inserted with the keys in the current node.
2. If the key is less than the smallest key in the current node, follow the leftmost child pointer.
3. If the key is greater than or equal to a key in the current node and less than the next key, follow the corresponding child pointer.
4. Repeat steps 2 and 3 until reaching a leaf node.
5. Insert the new key in the appropriate position in the leaf node, maintaining the sorted order.
6. If the leaf node becomes full after the insertion, split it into two nodes.
7. Move the median key to the parent node and insert the remaining keys as child pointers.
8. If the parent node becomes full after the insertion, split it as well.
9. Repeat steps 7 and 8 until reaching a node that does not become full after the insertion.

Maximum number of newly created nodes:

In the given question, the B-tree index has four levels, including the root node. This means there are three levels below the root node.

- At each level, the maximum number of nodes that can be newly created is equal to the maximum number of keys a node can hold, which is denoted by 'm' in the B-tree structure.
- In this case, we are not given the value of 'm', so let's assume it to be 'n'.
- Since each level has 'n' nodes, the maximum number of newly created nodes at each level is 'n - 1' (one less than the number of nodes).
- Therefore, in three levels below the root, the maximum number of newly created nodes is '(n - 1) * (n - 1) * (n - 1)'.
- Simplifying this, we get '(n - 1)^3'.
- As we are not given the value of 'n', we cannot determine the exact number of newly created nodes. However, we can conclude that the maximum number of newly created nodes is less than or equal to '(n - 1)^3'.
- Among the given options, the closest approximation to '(n