My company have no budget to take me required classes, question is...Must i need to take authorized institue class?
without class can i take VCP4 or VCP5 certification and become a Certified?
You MUST complete a pass to be certified. There are no exceptions to this.
Without the class, you can write the exam but you will not be certified. You can take the class later and complete your certification requirements - you don't have to take the class first although it will certainly be easier if you do.
If you have been working with ESX for only 3 months and have not yet started studying but expect to be certified in 2 weeks, you'll be disappointed because you're very unlikely to pass the exam. You will need a fairly significant amount of hands-on experience and even the required training is not adequate to prepare you for the test. If your company happens to have a fairly large ESXi environment with Enterprise Plus featuers (host profiles, distributed switches, etc.) with a mixture of storage technologies (NFS, iSCSI, FC) and a mix of ESX and ESXi you may have already run across some of the required background but if not, you have a lot of studying and practicing to do.