custom headers for category.php

 <!-- replace the below with this -->
 <a href="<?php echo esc_url( home_url( '/' ) ); ?>">
			<?php if (is_category(1)){ ?>
					<img src="http://asdfha.jpg" class="header-image" width="" height="" alt="Header 5" />
			<?php } else { 
				 $header_image = get_header_image(); ?>
				<img src="<?php echo esc_url( $header_image ); ?>" class="header-image" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" />
			<?php			} ?>
			</a>

header-snippet.php

/* this is the header.php file for twentytwelve, around line 48.  Replace this code w/ the lines above */

  	<?php $header_image = get_header_image();
		if ( ! empty( $header_image ) ) : ?>
			<a href="<?php echo esc_url( home_url( '/' ) ); ?>"><img src="<?php echo esc_url( $header_image ); ?>" class="header-image" width="<?php echo get_custom_header()->width; ?>" height="<?php echo get_custom_header()->height; ?>" alt="" /></a>
		<?php endif; ?>