It keeps shutting down randomly

If your fan is not working, then yeah, your laptop is going to shut down regularly from overheating. The fan may only need cleaning or it could need to be replaced, but either way you're going to have to open up the computer and remove the motherboard to get to the fan.

If it was my computer I'd probably go ahead and order a replacement fan before I started, but that's entirely up to you. If you take it apart and all it needs is cleaning, then yeah, you'll have a fan you don't need, but on the other hand if the fan is dead you'll be glad you have a replacement on hand. Of course, if you don't need the computer regularly then you can open it up first and find out, then order the fan if needed.

Anyway, the guides available on the device page for your Aspire are all used in the process of getting to the motherboard so you can follow them if you want, but for the complete fan replacement procedure you'll need the YouTube video I found showing you how to replace the fan.

Acer Aspire 5742 Disassembly / Fan Cleaning - YouTube