It makes backup and purges it.

bkp_purge.sh

#!/bin/bash
set -e

NOW=$(date +"%m-%d-%Y-%H-%M")
SOURCE_FOLDER_BKP=$1
DEST_FOLDER_BKP=$2

## Compacting and making backup
tar -zcf $DEST_FOLDER_BKP/bkp.$NOW.tar.gz  $FOLDER_TO_BKP

## Removing older than 5 days
find $FOLDER_TO_BKP -type f -mtime +5 -delete


## Usage
# ./bkp_purge.sh /home/path/logs/ /home/path/old.logs/