So I've bought a new laptop running Windows 10 and have installed Lightroom. I had previously been using an IPad and can't figure out how to sync my images with my new laptop. Surely I don't have to put all the images into a file and email them across or something......do I?!
When using the iPad, were you using the free version or did you have a subscription. If you have a subscription all your iPad images should already be in the cloud (tap on the Cloud icon on the main Lightroom screen to verify that it's saying "Synced and Backed Up"). If that's all OK, next question is which Lightroom app are you running on the laptop: Lightroom Classic or the cloud-based Lightroom? If the latter, you only need to start the app after signing into the Creative Cloud desktop app using the same subscription credentials as the iPad was using....Lightroom will automatically sync with the cloud and download previews for all the synced images.
If you're using Lightroom Classic instead, you need to enable syncing (click on the Cloud icon top right to start syncing). Once that's done all synced images in the cloud will automatically download to your hard drive (before starting, you might want to setup the location for those downloaded images via the Classic Preferences>Lightroom Sync tab as the default location is on your system drive).
If you were using the free version of Lightroom mobile on the iPad, you'll need to convert that to the full version by signing in using the subscription credentials, after which the app should start uploading the images to the cloud, and from there they should download into the Lightroom app on the laptop.
If that first screenshot is from your phone or iPad, it thinks you're still running a trial version. Try signing out and back in again, using the same credentials as used on the desktop app, to see if that kicks things into life.