<html>
<head>
<meta charset="utf-8">
</head>
<body>
<input id="lastName" type="text">
<input id="email" type="email">
<textarea id="textarea1" type="text"></textarea>
<button id="sendButton" disabled>Отправить</button>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script>
var pattern = /^([a-z0-9_\.-])+@[a-z0-9-]+\.([a-z]{2,4}\.)?[a-z]{2,4}$/;
$('#email, #lastName, #textarea1').keyup(function(){
$('#sendButton').prop('disabled', !pattern.test($('#email').val()) || $('#lastName').val().length<=5 || $('#textarea1').val().length<=5);
});
</script>
</body>
</html>
все просто, все условия надо проверить