Yes the 5S is a 64 bit. Adguard works nice when I'm connected on my wifi network but not when I use LTE network. There are ads everywhere in safari and apps. It certainly due to my mobile network provider because I compared with an other provider and adguard works nice.
Might be that your network provider enforces using of his own DNS servers (since Adguard Pro uses DNS blocking to block ads in apps). If it is possible, you can contact their support about it.
This doesn't explain why you have ads in Safari though, as they should be blocked by Content blocker. Send us a message to support from inside the app, just make sure to visit a website or two beforehand and launch some app that contains ads. Then post here your support userID (it is mentioned in the automatic email reply).
I have iPhone 7 with T-Mobile . Ad blocking in LTE mode simply doesn't work for me. It blocks ads in safari but if I open a website in chrome or in other apps, ads can be seen. In WiFi mode, this wonderful app blocks ads everywhere.