Framework laptops have the latest hardware, requiring a Linux kernel >= 5.12.

LMDE 5 "Elsie" is a Debian-based Linux Mint and ships with the 5.10 kernel. It'll install on a Framework, but it won't recognize the wireless card.

The easiest solution is to upgrade the LMDE kernel to >= 5.12,

Install LMDE 5

Install LMDE 5 as you would any other disto. You will need to provide a network connection. I shared my phone's Wi-Fi connection via USB. Once installed, log in. You still won't have Wi-Fi, so keep your alternative network connection running.

Upgrade the kernel

I chose 5.18.0-0.bpo.4-amd64.

sudo apt update -y
sudo apt upgrade -y
sudo apt install -y linux-image-5.18.0-0.bpo.4-amd64

Reboot.

Once the laptop comes back, login and update and upgrade one more time.

sudo apt update -y
sudo apt upgrade -y

Configure Wireless

You should get a notification asking you to configure your network. The wireless card is alive and it wants bytes.

Fingerprint Reader

Install software

I had to install gir1.2-fprint-2.0

sudo apt install -y gir1.2-fprint-2.0

Download required packages

Install in this order.

1. wget http://ftp.de.debian.org/debian/pool/main/f/fprintd/fprintd_1.94.2-1_amd64.deb
2. wget http://ftp.de.debian.org/debian/pool/main/libf/libfprint/libfprint-2-2_1.94.2-1_amd64.deb
3. wget http://ftp.de.debian.org/debian/pool/main/libu/libusb-1.0/libusb-1.0-0_1.0.26-1_amd64.deb
4. wget http://ftp.de.debian.org/debian/pool/main/f/fprintd/libpam-fprintd_1.94.2-1_amd64.deb

I find it's best to navigate to these files using your file browser and installing through the GUI versus using the command line.

Enable and enroll

Once your fingerprint reader is recognized, go ahead and configure the PAM configuration sudo pam-auth-update.

Now enroll your fingerprints sudo fprintd-enroll