Accessories for new runners

That's the thing I love about running... all you need is a good pair of sneakers and some clothes and you are all set. All the other stuff is fun to have, but not necessary. I do take my phone with me so I can listen to my tunes. And I have a water bottle sometimes, depending on the tempurature and the distance (either in my hand or in a belt I have). If I am running at work, I need my badge to get back in the building. I don't have a HRM because I think it would make me crazy. My hubs has one he uses when he bikes and loves it. In the summer months, I bring a white hand towel to dab my sweat and swat the horse/deer flies.

My must haves for running are:

GOOD running shoes
moisture-wicking clothing
Garmin GPS watch (mine has an HRM too which I use sometimes)
something to put music on (iphone, ipod)

when I was just running 5K I had good running shoes fitted for my feet, and a Nathan's 5K belt to hold my phone, sweat bands but really they were just bandanas, Polar FT7 and my Oakley M Frames. you won't need anything else. You really don't even need the HRM.

I'll second what everyone else has already said, and add in a good running bra. Seriously. I'm small busted and thought I could get away with el cheapo Walmart sports bras, and they worked okay at first, but as I run longer intervals I'm finding that they're just not doing the job anymore.

What accessories are recommended? watch? HRM? belt? Anything??

Shoes
Clothing - PRefer wicking and apropriate for your climate - Personally I prefer running tights to shorts most of the time and use high viz tops
Glasses - Generally with interchangeable lenses as appropriate

When the weather starts to get colder, hat and gloves

As you're talking about 5K for the moment that's about it. Once you've cracked the 5K distance you'll probably end up working up to 10Km and at that point you'll be making a decision about whether you want to focus on those distances or go longer. That's the point t start thinking about instrumentation. A GPS watch is a significant investment, so I really wouldn't advocate it in the short term.

You might want a handheld bottle, I've moved on to a fuel belt with a pouch for gels, keys etc and two 500ml bottles, although I generally only use it for longer runs of greater than 10K

I carry my phone in an arm strap.

One of the best things about running is that there is very little kit that you actually need, although quite a lot you might want.

fwiw I have an HRM, but rarely use it except for my long runs now.

I will echo what others said:

#1 - Properly fitted running shoes (don't just go with brand - just because it's a Nike/New Balance/Asics, etc. doesn't mean it's the right shoe FOR YOU). Go to a running store. Be prepared to spend $100-125. Your feet, ankles, shins, knees, hips, and lower back will thank you.

#2 - Running socks. These also can be pricey ($10/pair). I prefer "WrightSocks". Without proper running socks, I get blisters. Invest in 2-3 pair. Your feet will thank you again.

#3 - Proper running clothing. I prefer capri length pants because, well, my thighs are fat and if I wear shorts that don't create a barrier between them, the chafing - oh the chafing... it doesn't necessarily hurt when it happens, but when you shower afterward and the water hits it - oh goodness, it STINGS soooooo bad! If your thighs aren't fat, it might not be such a problem. (I have had the same problem with my fat arms if I run in a tank top - but that usually doesn't happen until I'm running more than 5 miles at a time). I'm working on all these things and my chubbiness is going away... my latest personal NSV was being able to run 2 miles in shorts without wanting to die when I took a shower.

Everything else can wait until you decide whether running is something you want to stick to or not. I had no other gear for my first several 10k runs... it was only when I started training for a half marathon that I bought a "fuel belt" (two small water bottles and a little pouch for my ShotBlocks). I didn't get a Garmin until I had been running for several years - and even then, it was used and my dad (who is a lifetime runner/marathoner) bought it for me for my birthday.

If it rains a lot where you live, a hat can be good to keep the sweat from getting washed into your eyes - again with the stinging!! yeeeouch.

I can't run without a hat or a visor. Keeps my hair out of my face and sweat from running into my eyes, in addition to keeping some of the sun off my face. In winter it helps block a little rain.

Other than that, after two years of running I always have

-good shoes
-wicking fabrics
-good socks (love my Smartwool socks!)
-HRM
-armband for my phone for tunes and running apps (I like Nike+ & Runkeeper)
-Road ID http://www.roadid.com/Common/default.aspx
-sunglasses
and of course, the hat.

I'm only echoing what others have said. Make sure you've been fitted for running shoes at a reputable local running specialty store. That's all you'll need for 3 miles. If you get through C25K and want to push the distance further, then you can start adding a Garmin, fuel belt, spibelt, more running clothes, etc. No sense in spending the money just yet.

Read this:
http://www.myfitnesspal.com/topics/show/1217573-so-you-want-to-start-running?