I have one of these. The phone (iphone 4s) slides/plugs into it and it is like a slightly bulky case. It doesn't say on it who made it but I bought it on eBay for under £10 and the small print inside says it is 'lithium polymer' capacity is 1,900mAH and output current is 500mA max.
It doubles battery life. I looked for the highest capacity unit but you have referred in your post to 5000mAH so you may want to check this isn't a stray zero!
And for what it is worth, I use Runkeeper and imagine it uses the same power as Strava, etc. To save battery life I fire it up, start my activity and immediately press the off switch - it then runs perfectly happily until I reawaken the phone. This gives me battery life easily well in excess of 4 hours. With the aux battery I'm still on full (phone) battery after over 4 hours riding.
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Cheers, Guy.
In the workshop:
Raleigh Team Pro - SB1988
Ribble 531C - "The Real Steel Special" - custom paint and Shimano stuff
GT Hardtail - Y2K frame plus hand-me-down parts
Campagnolo Master tool set (pre- plastic insert)