Edit in JSFiddle

<section class="header">
  <h1 class="header-title">ナビゲーションサンプルその2</h1>
  <p class="header-sub-title">スクロールするとタブがスライドするナビゲーション＆途中から固定</p>
  <div class="header-nav">
    <ul class="nav-tabs">
      <li><a class="nav-tab" href="#content1">CONTENT1</a></li>
      <li><a class="nav-tab" href="#content2">CONTENT2</a></li>
      <li><a class="nav-tab" href="#content3">CONTENT3</a></li>
      <li><a class="nav-tab" href="#content4">CONTENT4</a></li>
      <li><a class="nav-tab" href="#content5">CONTENT5</a></li>
    </ul>
    <span class="tab-slider"></span>
  </div>
</section>

<section class="contents">
  <div class="content" id="content1">
    <h2 class="content-title">CONTENT1</h2>
    <p>something about content1</p>
  </div>
  <div class="content" id="content2">
    <h2 class="content-title">CONTENT2</h2>
    <p>something about content2</p>
  </div>
  <div class="content" id="content3">
    <h2 class="content-title">CONTENT3</h2>
    <p>something about content3</p>
  </div>
  <div class="content" id="content4">
    <h2 class="content-title">CONTENT4</h2>
    <p>something about content4</p>
  </div>
  <div class="content" id="content5">
    <h2 class="content-title">CONTENT5</h2>
    <p>something about content5</p>
  </div>
</section>

.header,
.content {
	display: flex;
	flex-direction: column;
	justify-content: center;
	align-items: center;
	text-align: center;
	position: relative;
	height: 100vh;
	background: #eee;
	.header-title,
	.content-title{
		font-size: 1.5rem;
		margin: 0;
		letter-spacing: 0.5rem;
	}
	.header-sub-title {
		font-size: 1.0rem;
		opacity: 0.6;
	}
}

.header-nav {
	display: flex;
	position: absolute;
	bottom: 0;
	left: 0;
	width: 100%;
	height: 70px;
	box-shadow: 0 0 20px rgba(0, 0, 0, 0.1);
	background: #fff;
	z-index: 10;
		&.fixed {
			position: fixed;
			top: 0;
		}
}

.nav-tabs {
	display: flex;
	width: 100%;
	height: 100%;
	li {
		flex: 1;
	}
	a {
		text-decoration: none;
	}
}

.nav-tab {
	display: flex;
	justify-content: center;
	align-items: center;
	flex: 1;
	height: 100%;
	color: #000;
	font-size: 0.8rem;
	letter-spacing: 0.1rem;
	transition: all ease-in-out 0.5s;
	&:hover {
		color: #fff;
		background: #79c3bf;
		transition: all ease-in-out 0.5s;
	}
}

.tab-slider {
	position: absolute;
	bottom: 0;
	width: 0;
	height: 6px;
	background: #00a5a0;
	transition: left ease-in-out 0.3s;
}

class StickyNavigation {

  constructor() {
    this.currentId = null;
    this.currentTab = null;
    this.tabContainerHeight = 70;
    let self = this;
    $('.nav-tab').click(function() {
      self.onTabClick(event, $(this));
    });
    $(window).scroll(() => {
      this.onScroll();
    });
    $(window).resize(() => {
      this.onResize();
    });
  }

  onTabClick(event, element) {
    event.preventDefault();
    let scrollTop = $(element.attr('href')).offset().top - this.tabContainerHeight + 1;
    $('html, body').animate({
      scrollTop: scrollTop
    }, 600);
  }

  onScroll() {
    this.checkTabContainerPosition();
    this.findCurrentTabSelector();
  }

  onResize() {
    if (this.currentId) {
      this.setSliderCss();
    }
  }

  checkTabContainerPosition() {
    let offset = $('.header').offset().top + $('.header').height() - this.tabContainerHeight;
    if ($(window).scrollTop() > offset) {
      $('.header-nav').addClass('fixed');
    } else {
      $('.header-nav').removeClass('fixed');
    }
  }

  findCurrentTabSelector(element) {
    let newCurrentId;
    let newCurrentTab;
    let self = this;
    $('.nav-tab').each(function() {
      let id = $(this).attr('href');
      let offsetTop = $(id).offset().top - self.tabContainerHeight;
      let offsetBottom = $(id).offset().top + $(id).height() - self.tabContainerHeight;
      if ($(window).scrollTop() > offsetTop && $(window).scrollTop() < offsetBottom) {
        newCurrentId = id;
        newCurrentTab = $(this);
      }
    });
    if (this.currentId != newCurrentId || this.currentId === null) {
      this.currentId = newCurrentId;
      this.currentTab = newCurrentTab;
      this.setSliderCss();
    }
  }

  setSliderCss() {
    let width = 0;
    let left = 0;
    if (this.currentTab) {
      width = this.currentTab.css('width');
      left = this.currentTab.offset().left;
    }
    $('.tab-slider').css('width', width);
    $('.tab-slider').css('left', left);
  }

}

new StickyNavigation();