Does the select element have the required attribute?

Yes it has a required attribute, you can use it as follows

<select required>
<option value="" disabled selected>Choose</option>
<option value="first Option">First Option</option>
<option value="Second Option">Second Option</option>
</select>

Reference :

HTML Select required Attribute (W3C)

Yes you can use required attribute in HTML5. But remember, first value should be empty.

<select required>
<option value="">Please select</option>
<option value="first">First</option>
</select>

Here you get the more example:

http://dev.w3.org/html5/spec-author-view/the-select-element.html#the-select-element

You can do this way to make it look better

    <select required>
    <option hidden="" disabled="disabled" selected="selected" value="">Select subject</option>
    <option value="first Option">First Option</option>
    <option value="Second Option">Second Option</option>
    </select>