The most likely answer is no, you don't. However there are a few good reasons why 5.1 monitoring might be a good thing to have...
Firstly, you might record for the sheer pleasure of it. If you also have a liking for 5.1, then why not?
Alternatively, you might already be a successful composer and recordist supplying a client who requests 5.1 mixes. In this case, 5.1 monitoring is essential. As might also be the case if you are mastering DVDs yourself.
For everyone else however, 5.1 is simply not worth the expense nor effort.
Let's suppose you are still working towards your first success in the industry. Having a 5.1 showreel is not going to make the slightest bit of difference to your success. A DVD showreel might, but if your music and recordings don't cut it in stereo, 5.1 won't help.
Or suppose that you are getting deals for your music and you wonder if 5.1 would help you get more deals, and maybe more money on each one.
Well the plain fact is that if someone likes your music, they'll take it. If they need the recording as well, you will have to produce a professional quality stereo mix. If they like that, then they'll take it.
The reason why 5.1 is irrelevant in this case is that unless you are scoring or mixing an entire show or product, then your mix is going to have to sit comfortably with mixes of other people's music. Even in stereo that is unlikely to happen, so additional mastering will be necessary.
For 5.1, it would be better for the studio just to 'tweak' stereo mixes into 5.1, or for the ultimate control remix everything from the source multitracks.
5.1 in the home studio? The words 'red' and 'herring' come to mind. Unless you just like it of course.Come on the FREE COURSE TOUR