We increased volume on my Wife's 5c by going to Settings > General > Accessibility > Hearing Aids > Toggle on Hearing Aid Mode. This really worked a lot on her 5c. I did it on my 5 and it increased a small bit. But it made a huge difference on her phone.
Never considered the accessibility feature as you mentioned about the hearing aid feature so a good point to make.
I figured the easy way as many of us do is to raise and toggle using the external buttons on the left side holding it looking at it or left side depending on how it is being held. Good you made the point to cover all features and dependant just on what works best for the user or this case the OP.