Can I use the HTML5 <nav> element to group links that filter or reorder main content?

Our site has two main navigation links to two completely different pages. Something like that:

<section>
    <header>
        <nav>
            <ul>
                <li><a href="link1.html">Link 1</a></li>
                <li><a href="link2.html">Link 2</a></li>
            </ul>
        </nav>
    </header>
</section>

On one of the pages, we also have a filtering component made up of a list of links that Ajax uses to change the result set specified in the main content area (similar to how kayak.com filters its flight options in real time when setting sliders, check the boxes etc.)

My question is, should a group of filtering links be wrapped in an element <nav>?

It will look like this:

<section>
    <nav>
        <ul>
            <li><a href="#filter1">Filter 1</a></li>
            <li><a href="#filter2">Filter 2</a></li>
            <li><a href="#filter3">Filter 3</a></li>
            <li><a href="#filter4">Filter 4</a></li>
            <li><a href="#filter5">Filter 5</a></li>
        </ul>
    </nav>
</section>

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