First off, to answer the question, you have slightly limited options with an iPhone 5 since most carriers have taken that device off the shelf in favor of the newer models.
You may have more options getting a newer iPhone model like the 5s or 6
The iPhone 5s is still available from a number of carriers. Use this link to see all iPhone 5s 16 GB plans.
If you are wishing to stay with Verizon, I would contact them about upgrading your device and see what available options you have. As of this date, Verizon has an ongoing offer where you can get $100 off an iPhone 6 Plus 16GB/64 GB in Gold with monthly device payments.
Click here to Compare Verizon iPhone Plans
Now, If you are wishing to switch carriers, you have a lot of available options. You are basically open to any carrier on the map! Any carrier you are interested in, make sure you ask them their ongoing deals and offers - you may also want to consider buying an iPhone 5 or 5s through the used or refurbished markets. Local stores or online - Amazon, eBay etc
Click here to Compare all iPhones and Plans
Remember choosing different ways to pay such as through monthly installments, early upgrade lease or prepaid will make that hefty upfront cost affordably divided into a 24-month payment plan.