Functioning form on a cargo site?

I'm trying to create a form on a Cargo site, but they don't allow anywhere for .php files. I want the form to send an email to me upon the "submit" button being clicked. "mailto:" doesn't work, by the way.

Here's the form right now. I've tried adding an action to the form, but obviously I can't link a .php file:

<form>
<ul class="form-style-1">
    <li><label>Full Name <span class="required">*</span></label><input type="text" name="field1" class="field-divided" placeholder="First"> <input type="text" name="field2" class="field-divided" placeholder="Last"></li>
    <li>
        <label>Email <span class="required">*</span></label>
        <input type="email" name="field3" class="field-long">
    </li>
    <li>
        <label>Subject</label>
        <select name="field4" class="field-select">
        <option value="Advertise">Advertise</option>
        <option value="Partnership">Partnership</option>
        <option value="General Question">General</option>
        </select>
    </li>
    <li>
        <label>Your Message <span class="required">*</span></label>
        <textarea name="field5" id="field5" class="field-long field-textarea"></textarea>
    </li>
    <li>
        <input type="submit" value="Submit">
    </li>
</ul>
</form>

If anyone could suggest a workaround, I'd be so grateful!