Hi
1- should I upgrade Esxi hosts first or Vcenter
vCenter first before ESXi hosts.
2- can I use the existing licenses or I need to buy again for 5.5.
You can use existing license. As described in the KB here: VMware KB: Licensing ESXi 5.x and vCenter Server 5.x
"The vSphere 5.5 does not need new license keys. The existing 5.0/ 5.1 licenses will work and enable all the features of the software once upgraded"
See the vSphere 5.0 Upgrade Best Practices Technical Whitepaper - http://www.vmware.com/files/pdf/techpaper/vSphere-5-Upgrade-Best-Practices-Guide.pdf and also read the vSphere Upgrade Guide: vSphere 5.5 Documentation Center - vSphere Upgrade Guide
Please note that starting vCenter 5.1+ there is a new component in vCenter called vCenter Single-Sign On (SSO).
You might want to read about vCenter SSO here:
VMware KB: VMware vCenter Single Sign-On Server 5.5 FAQs
vCenter Single Sign-On Part 1: what is vCenter Single Sign-On? | VMware vSphere Blog - VMware Blogs
Allow me to introduce you to vCenter Single Sign-On 5.5 | VMware vSphere Blog - VMware Blogs