I'd like to be able to use a more powerful flash than the one built-into the Nex5n and the A6000. I can't stretch to top-flight stuff, I just need something fairly basic and straightforward to use.

Any suggestions, please?

I'm using the Nissin i40 on my A6500. Pretty powerful for such a small unit, fits very well on the camera. What I also love about it is that the flash head can tilt/swivel in any direction, allowing indirect flashing in almost any situation.

Thanks, Pieter, I'll have a look for that.

I don't know what kind of shoe(s) you camera(s) has but here is a comprehensive list:

https://www.mhohner.de/sony-minolta/flashes.php

It only has Minolta and Sony flashes, but the older Minolta flashes are great and inexpensive -- assuming it has the correct shoe for your gear. 

Edited December 31, 20222 yr by XKAES

The NEX-5N doesn't have a hotshoe. The a6000 has the newer Multi Interface Shoe. The older flashes that work on A-mount cameras need an adapter to fit on the a6000.

Big thanks again to Pieter, and also to XKAES.  All useful information!

Go to the reputable used market eg: local camera specialist or MPB etc.

You can usually pick up very good flash guns, dedicated to Sony, for a good price - mine cost around £30 each (i have 2)