JSFiddle - React, Tailwind, and code Playground

HTML

<nav>
        		<ul>
        			<li class = "cat1">
        				<a href="index.html">Meine Übersicht</a>
        			</li>
        			<li class = "cat2">
        				<a href="#">Tagebücher</a>
        				<ul>
        					<li><a href="#">Mein Tagebuch</a></li>
        					<li><a href="#">Neuer Tagebucheintrag</a></li>
        				</ul>
        			</li>
        			<li class = "cat3">
        				<a href="#">Profile</a>
        				<ul>
        					<li><a href="#">Mein Profil anzeigen</a></li>
        					<li><a href="#">Mein Profil bearbeiten</a></li>
        					<li><a href="#">Mein Profilbild bearbeitne</a></li>
        				</ul>
        			</li>
        			<li class = "cat4">
        				<a href="#">Rezepte</a>
        				<ul>
        					<li><a href="#">Alle Rezepte anzeigen</a></li>
        					<li><a href="#">Meine Rezepte</a></li>
        					<li><a href="#">Neues Rezept anlegen</a></li>
        				</ul>
        			</li>
        			<li class = "cat5">
        				<a href="#">Über uns</a>
        				<ul>
        					<li><a href="impressum.html">Impressum</a></li>
        					<li><a href="kontakt.html">Schreiben Sie uns</a></li>
        					<li><a href="agb.html">AGB</a></li>
        					<li><a href="datenschutz.html">Datenschutz</a></li>
        				</ul>
        			</li>
                    <li style="padding-top:5px; padding-left:15px; border-right:0px !important;">
                    	<form action="" method="get">
                        <input name="suche" type="text" placeholder="Suche ...." style="background-color:#efefef; border:0px; width:150px;">
                        <input name="abschicken" type="button" value="Los" style="border:0px; background-color:#efefef;">
                        </form>
                    </li>
        		</ul>
        	</nav>

CSS

nav {
    width: 900px;
	padding:20px;
}
nav ul {
    padding: 0px;
    margin: 0px;
}

nav ul:after {
    clear: both;
    content: " ";
    display: block;
    font-size: 0;
    height: 0;
    visibility: hidden;
}

nav ul,nav ul li{
    background-color: #C9CFD1;
}
nav ul li {
    list-style: none;
    float:left;
    border-right: 1px solid #FAFAFA;
}
nav ul li a {
    text-decoration: none;
    display: block;
    color: #333;
    padding: 7px 34px 7px 34px;
    -webkit-transition: background 0.3s ease-out;
    transition: background 0.3s ease-out;
}

nav ul li.cat1:hover a, nav ul li.cat1:hover > ul li a  {
    background-color: #FAFAFA;
}
nav ul li.cat2:hover a, nav ul li.cat2:hover > ul li a  {
    background-color: #FAFAFA;
}
nav ul li.cat3:hover a, nav ul li.cat3:hover > ul li a {
    background-color: #FAFAFA;
}
nav ul li.cat4:hover a, nav ul li.cat4:hover > ul li a {
    background-color: #FAFAFA;
}
nav ul li.cat5:hover a, nav ul li.cat5:hover > ul li a {
    background-color: #FAFAFA;
}

nav ul li:hover > a {
    color: #000;
}
nav ul li:hover > ul {
    visibility: visible;
}

nav ul li ul{
    display: inline;
    visibility: hidden;
    position: absolute;
    padding:0px;
}
nav ul li ul li{
	float: none;
}
nav ul li ul li a {
    color: #000;
}
nav ul li ul li a:hover{
	color: #333;
	background-color: #FAFAFA !important;
}