What would be a proper height of the bench for a 5 year old child (on a tall side)?

Are we talking about the same principle as for adults that forearms should end up relatively level with the keyboard?

Place where she is taking lessons uses just a regular bench, which needless to say, makes it rather awkward to reach the keys.

You could bring a pillow or something to boost height. I saw an article once suggesting stacking those square foam floor mat puzzle pieces for height. Also you could put a box or stepstool under their feet if their feet don't reach the floor. Their are stools specifically designed for that. I wouldn't be embarrassed to take these things to lessons if it helps your child do better at lessons.

It's very important for a young child to sit at the right height. It's also important to have a foot rest at the right height. My child's piano teacher teaches many young children and has both stackable seat cousions and height-adjustable foot rest.

Yes, totally agree with sarabande and MA.