Will new running shoes help with knee/foot pain?

I recently started running (about six weeks ago). It's VERY slow progress as I've never been a runner, so it's three days a week, short (5-8 minute) runs with walks in between. I'm experiencing some knee pain, and some mild foot pain after running and the next day. I've done other forms of exercise in the past (yoga, free weights, etc.) but I've been slacking off for the past couple of years, so I haven't really done much of anything besides walking. My running shoes are an older pair that were a hand-me-down from a friend. Asking experienced runners out there: will a new pair of running shoes help with the pain, or is it just something that is to be expected and it will get better with time and practice? It's not intolerable, but if I could lessen it by buying new shoes, then I will. Any input is appreciated.