We'll assume that your band does already have a web site, and talk about why that web site should be html5 based.
Over 70% of the smartphones owned in the US are either iPhone or Android based. Add to that the number of tablets in use now, and you start to see something very quickly. Computer web surfing isn't dead, but it's no longer the main means of consuming the web.
Mobile devices are now either tied with desktop website consumption, or have surpassed it (depending on who you talk to or what study you've read). But the point of this post isn't to mince those numbers. The point of this blog is compatibility.
Does your band's website work on these mobile platforms? If it's flash based, it'll work on Android phones and tablets just fine. But if it's flash based, it will NOT work on iOS devices such as iPhones, iPods, and iPads! By making your website flash based, you've effectively ensured that a major segment of those browsing the web on a mobile device will be unable to see your site.
This is why I believe web sites for artists should be made with mobile compatibility in mind from the start. After all, if I find a new artist and happen to be on my iPhone, I want to be able to listen to them regardless of my mobile device of choice. If I can't, I may never go back to check out that artist later.
HTML5 is a platform that will work on iOS devices. You now have websites being built with HTML5 formatting, and music players that are html5 based. For instance, Soundcloud.com and Reverbnation.com offer HTML5 music players that will work on iOS devices! I prefer Soundcloud because you can add .wav files for better overall sound quality, but that's just me. If you just want to stream an mp3, both sites will do the job.
Wix.com will let you build a website for free, and in exchange they will place a tiny "Wix.com" ad on the top and bottom of your site. But the good thing is that wix.com pages are typically HTML5 based! This means that the site will work perfectly on an iPhone or iPad, right down to the email form!
In short, make sure your website is compatible with mobile devices of all brands. HTML5 is a solid choice for this compatibility, but if another standard works for you and doesn't eliminate an entire popular operating system, then by all means use it. Just be sure it's compatible in the mobile market!