Transferring files from PC to PC thru USB (one monitor broken)

I have two Dell laptops. One I just bought (Newer Inspiron) and an old one from about 5 years ago (Older Inspiron). The older one has a broken monitor and you can barely see whats on the screen (text not legible). Is there a way I can get my files off the old laptop? It has no monitor output and just USB.

I'm sure that a computer shop could get them off but I wanted to try myself before I spent the money.

I also have a Mac if its easier to hook up that to the broken laptop instead.

Thanks.

Do you have an external enclosure? Or a hard drive adapter?
If it is not a bridged (box in the middle) USB cable you can't transfer files via USB. I would get a cheap external enclosure for ~$10 and use that.