How do I back up files from a mid-2009 MacBook Pro that can only boot into recovery mode?

You can try putting that laptop into Target Disk Mode to connect it to another Mac.

If you don't have the necessary cable, then the next best option would be to remove the hard drive and use a USB to SATA Adapter to connect the removed drive to another Mac. This assumes the hard drive is still healthy. Since you can boot into Recovery Mode, I would be the hard drive is failing.

If the hard drive is failing, then you have to be extremely careful since the more you attempt to use the drive, the more likely the drive failure will get worse where even a professional data recovery service will be unable to recover any data. I highly recommend having a professional data recovery service to attempt data recovery if the drive is failing. You usually only get one chance at recovering data from a failing hard drive, so choose wisely.

FYI, macOS and most data recovery utilities are unable to handle the I/O errors produced by a failing hard drive. Whenever I attempted to recover data from failing Apple hard drives, I always did so using a Linux system and special software to perform a block by block (bit for bit) low level clone that could ignore the I/O errors, then part two of the recovery process began. While I was highly successful, there were several close calls....and I knew what I was doing and the risks. Professionals have access to special expensive equipment & software which can make the process safer, plus they tend to fix any broken drive components as well.

If the drive failure is only just starting, then sometimes it may be possible to recover the majority of the data using macOS and regular software (definitely not the Finder), but you would first need to know the true health of that hard drive. Since you don't have a macOS boot drive, the only option would be creating & using a Linux boot disk.

Ryguy0 wrote:

I know. Issue is, I only got it from a family member this year, and she never backed it up, contrary to what she told me.

If she properly prepared to computer prior to giving it to you none of her data would be on the computer:

What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

I would also recommend going to a professional. I think this is a "data recovery" issue. I've done this before with a malfunctioning external drive (not an Apple product). The price was reasonable, but be prepared for this to take a while (overnight or longer). I was able to recover pretty much all or most of my data.

The other thing to watch out for: if the battery on that MacBook is old and on its last legs. I found out the hard way, with my old iPad Pro, that if the battery goes dead, you can't just plug in your device and have it work on AC power.

Apple won't replace batteries in some older devices. IME, it's hard to find trustworthy, non-Apple vendors to replace batteries in old devices.

If your device won't power on, you can't do anything with the contents (can't back it up; can't delete it).

Good luck!

The time to back up is before having computer problems. A major reason for backing up is to not lose data when computer problems happen.