I have an intel i5 chip. Yesterday I visited http://www.ubuntu.com/download/desktop and selected the 64-bit download option from the menu. The file which downloaded has the suffix '-amd64'. Is this going to work on my intel chip?
Yep. Sure will. I have to spend thirty characters saying "yes" here. So, "yes". :)
32/64 refers to addresses. 32 bits can only address ~4GB of memory. 64 bits can address a lot more.
Regardless of what OS you install, your CPU remains both 32-bit and 64-bit capable. If you install a 32-bit OS, you are limited to 4GB total memory, any more will be ignored, because the OS cannot address the memory.
If you install 64-bit OS, each process remains limited to 4GB, but the OS can handle as many as your installed memory will allow.
So don't worry, you have installed the correct OS bit.