Give the ul element a width - in this case it would be 600px, as you have 5 buttons * 105px width and 15px margin for each button. Removing the padding set on the ul and the left and right values set on the li, and give the ul element this style: 
.shortcut-buttons-set {
    margin: 0 auto;
    padding: 0;
    width: 600px;
}
ul.shortcut-buttons-set li {
    float: left;
    font-weight: bold;
    margin: 0 15px 0 0;
    padding: 0 !important;
    text-align: center;
}
Additionally, you'll want to use :last-child to remove the last 15px margin, so that the buttons are perfectly aligned. 
.shortcut-buttons-set li:last-child {
    margin: 0;
}
Taking this into account, the width for the ul should now be 585px.