Not sure about the specifics of Newstead Woods but if you live in Bromley and don't intend sending your DD to a Kent grammar you don't need to sit the Kent 11+. Bromley sets its own 11+ exams.
Some who want a back up option will also sit Kent 11+ with a view to gaining a place at Tonbridge Girls Grammar.
BTW exams are sat in September of Year 6, not Year 5. Many people start preparing their DC for the exams at the start of Year 5 - although not a great fan of tutoring myself it is often necessary to compete with everyone else who does it, especially if aiming for a school which selects on score.
Look at the elevenplusexams.co.uk forum - take a lot of what is said on there with a grain of salt, but there is useful advice too.
Bromley do not have 11+ exams - two schools in Bromley with selective exams are Newstead - girls sch and St olave - boys sch - however set by the schs themsleves not bromley council. Nearest boroughs with 11+ are bexley and kent - these have grammar schools which bromley do not. so your daughter will need to sit the exams for Newstaed - contact the school and list on the CAF.
There's also Sutton, which has several grammar schools, and Dartford Grammar School, which is in Kent. They all have different exams! It's worth knowing that Bexley expects parents to register their children for their tests before the start of year 6 - or they did a few years back. I assume this is to try and keep the out of borough numbers down a bit, as I can see no other reason for it.