If you take your current $5,600 at 5% and your $47,200 at 2.875 and calculate the weighted average you should wind up with a consolidated rate of 3.125%. If you take them separately in a 10 year repayment, your monthly would be $469.26 for 10 years. If you did them together at a 3.125% your monthly payment would be about $468.18. What you should be gathering is that you are pretty much in the same place over 10 years. Most of my kids want to keep their 2.875's out of the 5%'s etc like you but I would encourage you to do the math yourself and see if it really makes a difference in the long run and rethink the strategy of paying it all off provided it's federally backed (alternative loans are a very different beast). I'm not sure why other FA folks can't stress the risk (or lack thereof) on these loans and groom you all to "pay it off quick, it accrues interest etc" but that's all you hear. Every dollar accrues interest if borrowed or nets interest if invested, but not every loan has: unlimited deferment or forbearance, income contingent repayment, automatic death and total disability forgiveness. I should also mention that a Perkins in a consol loan would be unsub and thus the interest accruing is now yours so waiting until you will not be elgible to defer it makes sense but don't take that as a "never add it" premise since nothing is cut and dry in consolidating and if the rate for the consol is low enough, the extra interest accrued over the short period of time may still be less than if it sat out there and was paid back at 5%.
Let's say you owe $50,000 in a mortgage at 8.5% and your federal ed loan at 9.5%. Your first impulse (totally normal by the way) would be to pay the 9.5% first since it is costing you more. If you understand the risk of the mortgage which really is: you owe us so pay and if you are in arrears for 90 days, we want all $50,000 now (we foreclose). Oops, you can't do that since you were out of work for 2 months; we don't care. Now we get to sell your house out from under you since you can't pay us our $50,000 today. There is no "why" in lending: we at the mortgage company, car company, big screen TV company don't care why you can't pay us, just that you can't. The only loan type that cares "why" is federal ed lending.
Your federal education loan in the same situation would go more like this: you know you will be behind on the payments having been out of work for a month and call and request a forbearance since you have the intent to pay but not the ability. I grant you the forbearance and charge you the interest over the 3 months but more importantly: I don't ruin your life.
All that said, I'd be whacking my money on the mortgage and dragging out the fed loans with way less risk.
Perkins loans do have forgiveness which is largely centered around you going into teaching which you're pretty unlikely to do so consider what the forgiveness options really are and guage if they will ever apply to you and let that be factored in your decision whether to consolidate them or not. As for consolidation in general: not all repayment options are created equal and let's be perfectly honest about the fact that banks are in it to make money and not to help poor kids go to school (again, I'm also not sure why my colleagues believe the latter but they do...). Keeping the risk model in mind from above, let's say your repayment incentive is 1% off the rate after 36 payments. Does your monthly payment go own so you get the full 30 years or does the monthly stay the same and now you pay it over 22 years so it's "like the rate was 8.5%?" Would you rather have the longer repayment on the debt with the little to no risk factor? Maybe that means more than the 1% savings and thus enables you to take the extra money to put into the riskier debt...
I will repeat that alternative/private loans do not have the same options as federal education loans and discourage any of my kids from getting into those unless their backs were against the wall from day 1. The rates are low so they look attractive but the risk should discourage you from borrowing these types. If my alt loan was 6.5 and my fed was 7.5 I'd be paying off the alt loan that has an iron clad "you can only forbear for a total of 2 years throughout the term of the loan" you agreed to in the contract so if you burned through it already with residency etc, you're stuck later on if tragedy occurs. Sadly, I be amazed if anyone bothered to point this out to you but feel free to share.