How do I combine two content types in one Views block and get them to sort correctly? On my site, I have content types for Tradeshows and Webinars. I would like to have a block that shows the next 5 upcoming events by date, coming from either content type. I have Views set up to retrieve items from both types, and have the sort criteria set up with the date field from each type (they are different fields), in ascending order.  Ie., the Sort Criteria section looks like: Webinar Date (asc), Tradeshow Date (asc).

If I set the Views pager to display all items, I see a list of all the tradeshows, followed by the webinars.  It looks like Views retrieves the items from each content type, and sorts them correctly within their own group, but doesn't weave the two sets together, according to date.  This means that if I set the pager down to 5 items (the goal), then I'll only see tradeshows, since there are more than 5.

Is there a way to get Views to shuffle the two types together, and show the next 5 events, combined?

Edit: attaching screenshot
In the end, using hook_views_query_alter() turned out to be the simplest solution for my needs. I used code similar to that found in the solution below.

https://drupal.stackexchange.com/a/53128/18497