Will a 5.3 motor from a 2015 or 16 fit in my 2009 Silverado

Everything should bolt up but you'd probably have to use some parts from 09 engine.

The new engine comes with a computer should I use that computer or do I need to keep my 09 computer in it

Use the 09 Computer and electrical harnesses along with the manifold if they are different. If the sensors and harnesses are the same. I definitely use the 09 Computer. Make sure you inspect it for a Displacement on demand system as well. Because the if it has the displacement on demand system the lifters are different and you have the pull the cylinder heads off to change them to a standard lifter system. Also the control valves for the system are under the valley cover under the intake. So if you have a Displacement on Demand System and this 15 or 16 motor has it as well it should work but something to definitely inspect and know what system you have and what the 15 or 16 engine has. (Displacement on Demand shuts down 4 cylinders for fuel ecomony)