I prefer not to have to install 2 new switches in each room. Was going to leave the additional switch as standard.
While there may be exceptions, all of the "smart" 3-way light switches I know of need to be paired with a compatible - and much cheaper - auxiliary switch, and will not work with a conventional switch. I don't know which Lutron kit you're asking about, nor am I a Lutron user...so I'll use GE Link switches (which I do use) and current prices on Amazon.com as an example of what you'd need...
- GE 45613 Z-Wave Wireless Lighting Control Three-Way Dimmer Kit - $61.95 x 5 = $309.75
- A hub of some kind that can act as a Z-Wave controller. I use a 2nd Gen SmartThings Hub - $96.03
So, $405.78 for all 5 rooms. For most switches you'll also need at least one neutral wire in addition to the traveler wire you should already have. If your home isn't terribly old it should provide neutral wires at all wall switch boxes.
Note that even for a Lutron setup you'd need either a Lutron Smart Bridge (79.95) or a Wink Hub ($64.97) to control the switches, just like the ST Hub acts as the controller for my GE switches. Alexa would then interface with one of these vendors' cloud-based services in order to convert your spoken commands into instructions to control the switches.