If you were willing to tell us the rough geographical area, then you may find that there is a lot of fairly specific (though also hideously biased!) knowledge on here.
For day schools you are mainly looking at 3 types of entry -
a) 11+ (exams in Nov-Jan of Year 6)
b) pre-entry tests in year 6 or 7 followed by Common Entrance in Year 8
c) 13+ (exams in Nov-Jan of Year 8)
Your headmaster will not want you to go for option a. That does not mean that you should dismiss it. But for this first meeting, bear at the back of your mind that it isn't on the agenda. If you then come up with a list of schools which include ones which do take at 11+, then you need to consider whether that is a real option. Alas your headmaster will almost be professionally obliged to tell you to wait until 13, so you will need other sources of information and advice. In my experience there is no harm in going to talk to the registrar or even head of your target school. They will be very familiar with the dilemma of prep school parents, and will be ale to reassure you as to your best option. The other thing to look are fee levels. Some children stay at prep until 13+ as it is cheaper.
In terms of numbers of schools, it really depends on which route you choose. I would say that for route a, the average child seems to sit for 3, whereas for b, it seems more common to sit for 2. For route 3, again 3 would be the maximum, though it is a less common option to be honest. If your son does any music or sports scholarship assessment, then days are needed for these too, so sitting for 5 schools would mean 15 days of assessment (exam, interview, sports/music assessment) - possibly more with sport as some schools have a 2 stage assessment. It is a lot to try and fit in, and if you have clashes then you will be forced to show your hand early. And of course the schools talk to one another! Especially about scholarship candidates...
One reason as to why you need to understand which schools have which entry route is that typically for a and c Maths, English and Reasoning are tested, whereas with a CE offer, a lot of subjects are tested, and in particular languages can be an issue.