Use a higher than 230px logo image with 2013 theme

First of all, do not change any files in the twenty thirteen theme. The reason been, twenty thirteen is updated regulary, so if you made changes to the theme, you WILL loose everything you have done to the theme. You should create a child theme

You need to change the function that set the header height to get your image correctly cropped. This function can be found in ‘inc/custom-header.php’ on lines 30.

‘height’ => 230,

To change this, create a functions.php in your child theme, and add the following code in the functions.php you’ve created. This function will override the default heigh and set it to 500px

<?php
function my_custom_header_setup() {
    $args = array( 'height' => 500 );
    add_theme_support( 'custom-header', $args );
}
add_action( 'after_setup_theme', 'my_custom_header_setup' );

You can then just add the following style as you mentioned to your child themes’ style.css

.site-header .home-link {
        color: #141412;
        display: block;
        margin: 0 auto;
        max-width: 1080px;
        min-height: 500px;
        padding: 0 20px;
        text-decoration: none;
        width: 100%;
}