I assume the OP is asking whether she will need to immigrate at T3, make her own way to T5, and then go through immigration again. If she were on a "truly" international connection then, as you point out, she wouldn't, and could go through Flight Connections. However, since she is connecting to the Republic of Ireland, which is a unified border zone with the UK (i.e. there are no immigration controls between the Republic of Ireland and the UK so there will be no immigration on arrival in DUB), then she will need to go through immigration on arrival in Heathrow: http://www.heathrowairport.com/heath...lic-of-ireland. However, the bags themselves can be checked through and will not need to be retrieved and re-checked in London.


One other thing I would add to the list of conditions that have to be fulfilled is that the two flights must meet the Minimum Connection Time (MCT) requirements for Heathrow.