How to close the gap between my website title and subtitle?

Unless you provide a link to a page demonstrating the problem, no one will be able to offer much in the way of assistance.

Edit style.css:

#logo {
    bottom: 10px;
    height: 60px;
    margin-left: 5px;
    max-height: 60px;
    padding-top: 14px;
    z-index: 1;
}

and remove height: 60px;.

#headerwrap {
    height: 100px;
}

Reduce that height value.