Nope. Qlikview Desktop cannot act as a webserver, not even for cell phones. You need Qlikview Server and you need Qlikview Workbench. Perhaps you should investigate Qlik Sense and see if you can create simple Qlik Sense apps that you are willing to publish on Qlik Sense Cloud. You can share those apps between the five users so they can access them from their phones if these phones have a browser that supports html5/
You can use Qlik Sense Desktop for free and still share your apps between the users of Qlik Sense Desktop. You can also sign up for a free account of Qlik Sense Cloud and share apps published there between five users. There is a limit for the size of the apps and the data files you upload into Qlik Cloud. So it looks like you could use Qlik Sense for free in your case with those five users as long as you stay within the data size limits. If you need more than that you can sign up for Qlik Cloud Plus of Qlik Cloud Business if you're willing to pay the subscription costs for those services. See Pricing and Implementation for more information.
I have no idea if it will be better for you. If you buy a Qlik Sense Enterprise Starter Pack with 5 tokens you'll have enough for your five users and complete control over your Qlik Sense server installation. It will save you the hassle of reloading documents locally and the upload them into the cloud. Buying a starter pack certainly is not free, but the price is quite reasonable imho.