In addition to make one visible, you have to make the four others invisible as well.
A better solution to the if..else spaghetti code would be to have the labels in an array, and define a function to make the label with specified index visible (implying the four others labels invisible).
private void MakeVisible(int index)
{
for (int i = 0; i < theLabelArray.Length; ++i)
{
theLabelArray[i].Visible = (i == index);
}
}