Edit in JSFiddle

<section class="header">
  <h1 class="header-title">ナビゲーションサンプルその3</h1>
  <p class="header-sub-title">TOPで固定表示→特定の位置までスクロール→ナビゲーション変化</p>
  <ul class="header-nav">
    <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>
</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: fixed;
  top: 0;
  width: 100%;
  height: 70px;
  box-shadow: 0 0 20px rgba(0, 0, 0, 0.1);
  background: #fff;
  z-index: 10;
  transition: all ease-in-out 0.5s;
  	li {
		flex: 1;
		height: 100%;
	}
  	.nav-tab {
  		display: flex;
  		justify-content: center;
  		align-items: center;
  		flex: 1;
		height: 100%;
  		color: #000;
  		letter-spacing: 0.1rem;
  		transition: all ease-in-out 0.5s;
  		font-size: 0.8rem;
		text-decoration: none;
	}
	.nav-tab:hover {
		color: #fff;
		background: #79c3bf;
		transition: all ease-in-out 0.5s;
	}
}

.header-nav.transform {
	height: 90px;
	background: #79c3bf;
		.nav-tab{
		 	color: #fff;
		}
		.nav-tab:hover{
			color: #000;
			background: #00a5a0;
		}
}

let _window = $(window),
    _nav = $('.header-nav'),
    headerBottom = $('.header').height();

_window.on('scroll', function() {
  if (_window.scrollTop() > headerBottom) {
    _nav.addClass('transform');
  } else {
    _nav.removeClass('transform');
  }
});

_window.trigger('scroll');