The equals sign is going to confuse url parsers since it has special meaning.
If you were to change your route to:
routes.MapRoute("CustomerOrder", "CustomerOrder/{action}/{id}",
new { controller = "Order", id = "" });
Then the following view code
<%= Html.MenuItem("Back to List", "Index", new { customerID = 5 })%>
Would create a link to:
CustomerOrder/Index/?customerid=5
which would work just fine.
Note
Given your current routing configuration, you would get the exact same results by deleting your CustomerOrder route since it is broken and you get the desired results from the default route.