Create separate MD5 files recursively for each file

I've always wanted to keep an eye on my file storage and keep an eye out for damage over time when files get damaged.

For this, I'm trying to write a bash/shell script for Linux that recurses through directories and creates an MD5 hash and file for each file, each in the same directory. I'm not a fan of a single file that contains all the hashes, as it would all tip over if a single file kept becoming corrupted or lost.

- Directory 1
    - TestFile.txt
    - TestFile.txt.md5
    - AnotherTestFile.wav
    - AnotherTestFile.wav.md5
- Directory 2
    - MyDetails.docx
    - MyDetails.docx.md5

I've tried using md5sumthe command in multiple ways, but it always wants one:

1. Creates all hashes in one file.
2. Each file creates a separate .md5 hash file, but the filename in the MD5 hash file contains the full file path (eg ./Documents/Directory1/TestFile.txt), not just the filename (eg TestFile.txt).

I have tools on Windows that do this( MD5Checker), but it is hashing files on my file server on the network. I'd rather think of something that can run natively on a Linux OS.

Any ideas?

My latest attempt (I know it's bad)

It creates MD5 files, but the file path in the hash and the file is the full file path, not the base file path.

#!/bin/bash

function md5_dir {
for file in $1/*;
do
        if [[ -f "$file" && ! $file == *.md5 ]];
        then
                file_basename=$(basename "$file");
                echo "$file" "$file_basename";
                md5sum "$file" > "$file.md5";
        fi;
        if [[ -d "$file" ]];
        then
                md5_dir $file
        fi;
done;
}



echo "$1"
md5_dir "$1";