Q: Time to buy a new computer?

You describe something that sounds like the fan is wearing out, it could be the hard disk (assuming it is not an SSD) or possibly the CD/DVD drive. It would be best to find an Apple service centre that can check it out & replace the failing parts if possible.

Apple stores are easiest they will charge since it is beyond any warranties, but you should get a free consultation at the genius bar to give you a quote.

You can ignore it if you like but it may get worse & you could lose data if you don't have good backups.

Fans speeding up is a sign of several things. The significant ones are:

1) One of the fans has failed forcing the other to do twice the work. Use the original disks that came with your computer to run Apple Hardware Test. It will detect failed/failing fans with a "4MOT" error. Using Apple Hardware Test - Apple Support

2) Runaway back ground applications. Please see: Apps can affect Mac performance, battery runtime, temperature, and fan activity - Apple Support

We really need more info on your MBP's variant including if you have any known bad software packages (like anti-virus software) that slow your computer and run up the temps. The easiest way is to download and install this free utility:

http://www.etresoft.com/etrecheck

It is secure and written by one of our most valued members to allow users to show details of their computer's configuration in Apple Support Communities without revealing any sensitive personal data.

Run the program and click the "Copy report to clipboard" button when it displays the results. Then return here and paste the report into a response to your initial post. It can often show if any harmful files/programs are dragging down your performance or causing the fans to work overtime.