I'm not a super photo person, but fwiw, here are my tips. I don't have the Sony, but dpreview has a
good review. The color charts and macro distortion are worth looking at. The Oly I do have, so I can actually speak from experience.
Apologies in advance if you know this stuff already.
Color
Get to know your camera's quirks. It's likely that auto white balance will not be good enough for photographs under lights. The Oly 510, for example - AWB is a gamble anywhere except under full sun.
If you're lucky, there'll be a preset WB that is close enough. Better still, set your white balance manually. On the Oly, you can also scroll through Kelvin numbers til you hit a good one. The LCD screen is wonderful because you can see the WB effect as you scroll through the options.
You may still have issues with purples and blues, especially on the H5.
You can always do a little adjustment on the computer afterwards, but it's limited. If on the Oly you shoot/save the images in RAW format, you'll have more ability to adjust the color.
Focus
These cameras think they know where you want to focus. Well, they don't. You decide where the auto focus is going to be - in the middle. (I assume there's a way to do this on the H5. On the Oly, you can pick one of three.) Then, you can decide if the pouch or the dorsal is going to have the best focus. Once you have it in focus, you can move the camera (with some risk of losing focus). If the end product is going to be a small image (like on the web), then you may be better off leaving the object in the middle and cropping the image later.
Macro distortion
According to dpreview, looks like you'll get a fair amount of distortion using macro at the wide end, and you'd be better off zooming in a little first.
Lighting
There are good tips in the link above.
This might also give you ideas for a diffuse light. I hate dealing with lighting unless I have time to shoot and check and re-shoot, so usually I go the no flash route.
Shake
If your hands aren't too steady, or you're shooting in low light conditions, put the camera on a tripod or any stable surface. If you have a remote, or a timer, use that to take the picture instead of pressing the shutter button.
The image stabilization in the Oly is pretty good, but not good enough for macros of tiny things......