I am putting a long continuos handrail along the closed wall of my stair but need to know what is required at the bottom where 5 steps are open on the other side?
For new construction, over 3 rises requires a railing to code (can't pass a 4" sphere). At a minimum I'd think you'd want a continuous handrail (extending to a newel post) for safety. I had a similar situation in my previous home, and I did exactly that. It was never a concern for small children in my case, and the inspector at sale didn't flag it.
If you can't switch your rail to that side, consider a newel post and rail to the end of the wall, even without balusters.
There are some differences among various building codes but typically the handrails must continue at the same height following each step and landing plus one tread length distance at the floor or ground. This last section is called the return if one stair connects to another.
Think of it as a continuous parallel line at the same constant height. Outdoor landings or landings suspended over dangerous areas are often required to be higher for added protection. Variations are possible by jurisdiction and use.
If you measure from the top of the tread where the riser meets the tread to the top of the existing handrail - that is the height you should maintain across your landing.
The transition angle between landing rail and stair rail is most easily determined by simply extending these lines, drawing it full-scale if possible.