Add following snippet into your ajax success.
if ($('.your_slick_selector').hasClass('slick-initialized')) {
$('.your_slick_selector').slick('destroy');
}
$( '.your_slick_selector' ).html( response );
$( '.your_slick_selector' ).slick({
infinite: false,
slidesToShow: 5,
slidesToScroll: 5,
});
