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You might try this kind of approach (untested):

add_action( 'pre_get_posts', function( $q )
{
    $exclude_cats = [ 12, 34 ]; // <-- Edit this!

    if(    ! is_admin() 
        && $q->is_main_query()
        && ! is_singular()
        && ! is_category( $exclude_cats ) 
    )
    {
        $exclude_post_ids = get_posts( 
            [
                'fields'         => 'ids',
                'posts_per_page' => 5,
                'category__in'   => $exclude_cats,
            ]
        );
        $q->set( 'post__not_in', (array) $exclude_post_ids ); 
    }
} );

where you might have to adjust this further to your needs.

You might try this kind of pre_get_posts hook approach (untested):

add_action( 'pre_get_posts', function( $q )
{
    $exclude_cats = [ 12, 34 ]; // <-- Edit these category ids!

    if(    ! is_admin() 
        && $q->is_main_query()
        && ! is_singular()
        && ! is_category( $exclude_cats ) 
    )
    {
        $exclude_post_ids = get_posts( 
            [
                'fields'         => 'ids',
                'posts_per_page' => 5,
                'category__in'   => $exclude_cats,
            ]
        );
        $q->set( 'post__not_in', (array) $exclude_post_ids ); 
    }
} );

where you might have to adjust this further to your needs.

You also might want to use category slugs instead, but then you would have to setup a proper tax_query, since category__in only supports an array of category ids.

You might try this kind of approach (untested):

add_action( 'pre_get_posts', function( $q )
{
    if( ! is_admin() && $q->is_main_query() )
    {
        $exclude = get_posts( 
            [
                'fields'         => 'ids',
                'posts_per_page' => 5,
                'category__in'   => [ 12, 34 ] // <-- Edit this!
            ]
        );
        $q->set( 'post__not_in', (array) $exclude ); 
    }
} );

where you might have to adjust this further to your needs.

You might try this kind of approach (untested):

add_action( 'pre_get_posts', function( $q )
{
    $exclude_cats = [ 12, 34 ]; // <-- Edit this!

    if(    ! is_admin() 
        && $q->is_main_query()
        && ! is_singular()
        && ! is_category( $exclude_cats ) 
    )
    {
        $exclude_post_ids = get_posts( 
            [
                'fields'         => 'ids',
                'posts_per_page' => 5,
                'category__in'   => $exclude_cats,
            ]
        );
        $q->set( 'post__not_in', (array) $exclude_post_ids ); 
    }
} );

where you might have to adjust this further to your needs.

You might try this kind of approach (untested):

add_action( 'pre_get_posts', function( $q )
{
    if( ! is_admin() && $q->is_main_query() )
    {
        $exclude = get_posts( 
            [
                'fields'         => 'ids',
                'posts_per_page' => 5,
                'category__in'   => [ 12, 34 ] // <-- Edit this!
            ]
        );
        $q->set( 'post__not_in', $exclude ); 
    }
} );

where you might have to adjust this further to your needs.

You might try this kind of approach (untested):

add_action( 'pre_get_posts', function( $q )
{
    if( ! is_admin() && $q->is_main_query() )
    {
        $exclude = get_posts( 
            [
                'fields'         => 'ids',
                'posts_per_page' => 5,
                'category__in'   => [ 12, 34 ] // <-- Edit this!
            ]
        );
        $q->set( 'post__not_in', (array) $exclude ); 
    }
} );

where you might have to adjust this further to your needs.