Latency will go down with 5G if you pay for it. How much is the big question.
There are 3 sides to 5G:
- eMBB: massive boradband --- high throughput, mmWaves;
- URLLC: ultra reliable and low latency, for industrial applications typically;
- mMTC: massive IoT. Cheap and low power.
The network can handle all 3, but as a device or user that doesn't mean you'll get all the benefits at the same time, some choice will be required. The reduced latency always has some cost impact.
Today the LTE air latency is 4-5 ms, the rest is in the core network. 5G has some air interface changes to reduce the air contribution to 1 ms, in the context of URLLC. For basic users, it'll likely be like LTE (already pretty good). There may be some general improvement if they optimize the core latency for all, but TBC.