Can I create a new story type that when created also create 5 child tasks

You can create a workitem template that creates the story and its children all at once

then the user would create workitem from template instead of create workitem.

You can do this one of two ways:
1) write a server-side participant to create the child work items
2) create a template which includes the Story parent AND all of the children. 

#1 is a bit more work and requires deployment of a plugin.  However, it works more like what people would normally work, by using "Create work item".

#2 can be done without any programming or deployment of server extensions.  However, your users will have to use "Create work item from template" and select the template and then it creates all 6 work items with "default" text.  They then have to know to go into the Story and update the description/summary/attributes to be correct.

There is alot of information on the web and in articles about creating a plugin.  Templates have a few articles (here is one: https://jazz.net/products/rational-team-concert/features/wi).

 See also Using a template to create work items.