In woocommerce we can add the fixed discount automatically of 10% if the cart total equal 5000 or greater than 5000

add_action( 'woocommerce_cart_calculate_fees', 'discount_based_on_cart_total', 25, 1 );
function discount_based_on_cart_total( $cart ) {

    if ( is_admin() && ! defined( 'DOING_AJAX' ) ) return;

    $total = $cart->cart_contents_total;

    // Percentage discount (10%)
    if( $total >= 5000 )
        $discount = $total * 0.1;
    // Fixed amount discount ($20)
    else
        // $discount = 10;

    // Add the discount
    $cart->add_fee( __('discount', 'woocommerce'), -$discount );
}

Just paste the code in your functions.php file of theme and check it is working or not.

Thanks for visting and comment below if it is useful for You!!!!