Brando Shopping sell a great case for the fitness types or those that like having a case strapped to their arm. Whilst this case is stated as being waterproof I would be careful as rain could come thru from underneath via the flaps as shown on the photos. Showerproof more likely I would have thought.

The official specs are –

Features
Lightweight, breathable neoprene material
With earphone port opening
Ultra comfortable
Keep your device secure while running or workout
Easy adjust to fit your arm
Waterproof transparent plastic cover
Length: 43.7cm

Colours
Black
Pink
Blue
Red

Compatible Models
iPhone 5
iPhone 5c
iPhone 5s

I’ve used this quite a bit whilst walking my dogs and have found it really handy.

Available from Brando Shopping.