We were all noobs once, welcome and I hope someone double checks my math.
5 x 3.7 = 18.5
I would suggest you find something with 19VDC and 1000mA. How easy was that? If you have an old wall wort hanging around try that.
For something permanent and/or something you really want to last...be nice...ultra reliable, then look to a "real" driver.
http://www.ledsupply.com/xi-led120a0700c24f.php
The above offers 700mA versus your 1000mA, I am not sure you would really notice the difference in brightness or you could live with the slightly lower brightness. This is a quality piece of equipment and no need for Buckpuck. That said, there is a 1000mA driver....LED-120A-0024V-10F. I can't find it right now, but somebody sells it.
http://www.ledsupply.com/ld-mdu9-sc-3570.php
The above is what I am using to drive 4 Seoul P4s at 700mA right now because a power hickup drove through an old laptop power brick that was feeding a Zane dimmer then going to the Seouls. Whenever that hickup happened, it burnout all 4 Seouls at the same time. The above driver is plenty bright for under counter lighting at my kitchen desk area. I think I am going to go to 350mA shortly, these things really power LEDs well.
In conclusion, I really don't think I am going to use wall worts much anymore. Yes, they work and work well. I just want that confidence that my project will perform and work just as I want it to. So as long as you have the cash, I recommend a real drive like the ones above. Money tight: find an old wall wort, make sure it puts out DC, feel good about saving money and prepare for it's future death......hopefully it will just die and not take everything else out too.
I can recommend LED Supply, I have ordered from them around 5 or 6 times now with no problems ever. Perhaps others will chime in with their favorite vendor too.
Good luck, let us know how this project works out. Love to see pictures of the completed project.
Bob E.