Add this in your button click method:
string[] parts = yourTextBox.Text.Split('#');
yourListBox.Items.AddRange(parts);
If you don't want that there can be empty elements in your listbox, try this:
string[] parts = yourTextBox.Text.Split(new char[] { '#' }, StringSplitOptions.RemoveEmptyEntries);
yourListBox.Items.AddRange(parts);
If you want to add 5 items on every button click (and only want 5 items in the listbox), try this:
int i = 0;
void yourButton_Click(object sender, EventArgs e)
{
string[] parts = yourTextBox.Text.Split(new char[] { '#' }, StringSplitOptions.RemoveEmptyEntries);
string[] partsToAdd = parts.Skip(5 * i).Take(5).ToArray();
yourListBox.Items.Clear();
yourListBox.Items.AddRange(partsToAdd);
i++;
}