Do you have a longer arrow on hand to make some measurements with? To measure your draw length, you can take an arrow shaft and draw a ring around it at various distances from the valley of the nock. I'd use different color sharpies and start at 27" and draw a ring every 1/2" out to 30".
You'll need someone to watch you shoot. The different colors will make it easy for them to see how far you're drawing the bow. Shoot several times and have them take note of the color ring you pull to. Just standing, pulling the bow back, and having someone mark the shaft on the back of the riser might also work, but it's much better to see what you pull when you shoot.
As to your arrows, you're probably going to have to go with a much heavier head. And, unfortunately, the arrows are probably too short for you to use broadheads. It's a good idea to get shafts that are at least 1/2" longer than your draw for broadheads, but 1" longer is better.
We need to know what your draw is to make some accurate suggestions, but I can tell you that a 28" 5575 with a 125 grain point spines out to around 97-99 pounds. That is really too stiff. Not to mention that they are really light. If you pull that bow to 29", you'll need a 30" arrow, and probably a 150-175 grain head. To get the arrows you have to work, you'll probably need to use a 225 grain point. Again, they'll be too short to use broadheads on. You don't want to have a broadhead hitting your riser.
It would be good to find a scale to accurately measure the poundage of your bow, but if you can't, you can figure that a bow will gain around 3# for every inch of draw over 28", up to a point. Some bows will start to stack at longer draws. If your draw is 29", you should be okay.
For a hunting weight arrow, you really want to try and have your arrow weight around 10 grains per pound of draw weight. So, if you're pulling 58# at your draw, you'll need at least a 580 grain arrow. Your current 5575s will weigh around 530 grains with a 225 grain head. That is a little over 9 grains per pound. I wouldn't recommend going lighter than that. Going too light in weight can harm your bow, too.
I have a feeling you're going to have to go with a different shaft. Personally, I'd recommend getting some Arrow Dynamics Traditional shafts. They are a very forgiving shaft and will allow you to use a variety of weight points. They're heavy enough to get you the weight you need. They're also pretty tough, too. I've got a bunch of GT 5575s and GT 7595s, but pretty much the only carbon I use are the Arrow Dynamics shafts. They are just so forgiving and easy to tune.