My Uploads directory is 19GB and /logs is 5.5GB of that. Can I clear some of this out, especially interested in the logs if it's not required?

Are the recent files also so huge? I would suggest to submit a ticket if you have a latest.php file and a 2016_04_25.php  . I'd like to take a look at them if you don't mind.

 

And it's save to delete the old log files. You should also review your log prune settings. ( ACP => System => Support System Log ; on top if this page there's a prune settings button. Make sure that you're pruning your log after X days)

 

That was set to 'never' so I've set it to 30 days. Thank you. 

I'll submit a ticket now