You're awesome Halley! Congratulations on your first 5k!
Everyone has given you some excellent advice and yes, shoes, along with proper running form should be high on your priority list to prevent injuries.
When I first started running, I not only had a lot of knee pain, but I also had a lot of lower back pain too, even after purchasing a $110 pair of shoes. I've been told, and I can attest that both these are "normal" for new runners. As far as the lower back pain, one thing to consider is your core strength. In other words, how strong is your mid section?
As your body begins to strengthen, and it will do so quicker than you think, but the back pain will start to subside unless you increase your mileage substantially in a short period of time which simpy invites injury, so resist the temptation lol. In the meantime, to help reduce fatigue on your back when you run, keep your thumbs up (Not pointing up like your being cool lol) and don't let your arms swing in front of your abdomen.
You'll notice that as you tire, your head drops, your shoulders hunch forward, your thumbs turn inward and your hands start to swing in front of you. It's natural... we all do it, and it's hard on your back.
When your shoulders hunch and your arms swing in front of you, it puts pressure on your lungs and on your heart. I can raise my heart rate by almost 5-8 beats per minute just by hunching my shoulders foward, dropping my thumbs horizontal and swinging my arms in front of me instead of next to me.
Think of it like this, and give it a try. Stand straight up and swing your arms like a tin soldier back and forth with your elbows locked. It's pretty easy and notice that it doesn't require any back muscles. Now, as your swinging your arms, start to bring them in front of you. Not only does it take away from your forward momentum, but it puts an added demand on your back.
So, try this next time you run. Keep your thumbs up, your shoulders back and don't let your arms swing in front of you. By doing so, it keeps your momentum moving forward while lowering your heart rate and over all, makes you a more effective runner. Give it a shot and congratulations on the running bug!
Jeff