lost all my photos when my apple Mac crashed and I had to purchase a new one

When it comes to backing up a computer redundancy is wise. Why, because (as you have found out) backups can fail too. What many experienced users on these forums (myself included) do is to have 2-3 backup EHDs and do the following:

1. Time Machine #1
2. Time Machine #2 (this should be a Time Machine backup External Hard Disk that you backup on anywhere from 1x per week to 1x per month) and then store it outside your home so it is safe in the event of a home disaster.
3. Bootable Clone using either SuperDuper! or Carbon Copy Cloner to clone the internal drive. SuperDuper! or Carbon Copy Cloner it does not really matter as both do the same thing, they create a clone of the internal drive. You can set them up to schedule when the backups occur (I use SuperDuper! and backup nightly about 3AM and only backup new or changed files) which is handy and wise.

If you don't know about Time Machine that is Apple's backup app, you can learn about it in Back up your Mac with Time Machine. This does hourly backups of new and changed files. It is an excellent tool and EVERY Mac user should be using Time Machine!!!!!!!!!!!!!!!!

First things first. You want to protect the photos you may still have, so start by putting that old backup drive aside for a moment.

Now, get another new (or new-ish) external hdd or ssd that you will set up and let Time Machine use as your new backup device for your new Mac. Use a drive that is 2x-3x the total capacity of the startup drive on your new Mac.

Back up your Mac with Time Machine - Apple Support

After that, consider cloning the old drive onto one another hdd of equal or greater capacity. Clone your old back up as insurance should something happen to that hdd with your precious photos. If the drive is healthy you should be able to clone it with an app like Carbon Copy Cloner or SuperDuper!

Now you can work with the either the clone drive to find a path to recovering the photos that are missing.

You might find a way to access the data from another older Mac/macOS. You might find it to be accessible with certain drive utility/data recovery apps.

Maybe a trip to an Apple Store Genius Bar with your devices can help shine a light on other options.

You can make a Genius Bar appointment for hardware/software service and support using this link:

Contact Apple for support and service - Apple Support

Whatever you decide, now you can take a breath and take your time finding the way to recover your photos.

Where did you think they backed up to? Did you have iCloud Photo Library enabled?

Were you using an external drive and Time Machine to backup you Mac?

If you were using iCloud Photo Library and you did not have sufficient space available to sync all of your photos, and you don’t have a Time Machine or other backup containing the photos, the only place left to recover them from would be the original Mac.

Since you don’t explain what happened other than it “crashed”, or whether you even still have the old Mac, it’s hard to make any recommendations.

What year and model was the old Mac?

What version macOS was it running?

Is that a backup on a CD disc or is it on a hard drive?

Do you know how that backup disc was created?