I think you may have more than the option you've outlined:
If you've owned the home you're in now for a while, you might have equity for a loan that will put you into a 20%down position. So, that means if the value of the home you are in is higher by a significant amount than the loan you're paying down on, then you should be able to take the value of the home in a home loan, use it for the downpayment on the new property and go from there.
Another option is to sell the home you're in now. Again, this is favorable if you have good equity in your home. It would take time to sell your home, depending on the neighborhood and condition of the property. I would say though, that once you sell it and get the proceeds from the sale, your position might be pretty good at that time. It all depends and you'd need to talk to a financial advisor to see what all the benefits are. I know that if you sell the home you're in now, you won't have to worry about managing the tenant that moves in.
And of course, you can keep the property you own now, rent it out and use it to help pay a mortgage. This allows you to hold on to a valuable home, while living in a condo of your choice.
Can you get a 5% or 10% loan? The short answer is yes you can. The long answer is that not a lot of people are being awarded such loans right now. You can go the FHA route, but that will also take time, and you will have to be precise with whatever they ask of you - not to mention that the property you buy has to be approved by FHA. You'll have to Mortgage Insurance and there are many ways to do that as well (like paying it all up front, or paying it monthly with the mortgage, or deferring it until you sell one of your properties - all have pluses and minuses regarding taxes and how you can take them as deductions). Talk to a mortgage professional as soon as you can.