We had secondary infertility too OP. 5 year gap between 1 and 2 achieved via IVF, and then managed a natural 3 year gap between 2 and 3 (having had a couple of failed IVFs and then conceived naturally, go figure).
Just to offer a slightly less positive perspective (as others have pointed out the advantages) - I will be absolutely honest and say I have found the age gaps tough. There is no real relationship between DS1 and 3, the gap is too big, but that is also in part due to (a) DS1's personality and some additional needs and (b) due to the fact that DS3 gets on really really well with DS2 which invariably affects the overall relationships because there are 3 of them.
Personally speaking I found it was really lovely for the first few years, when DS1 was in primary, DS2 in nursery and DS3 a baby. Everything just kind of flowed. It got more challenging as the years went on - I found the age gap between DS1 and the others felt like it doubled once DS1 went to secondary, for example, and once the baby was a toddler it was a lot harder! I reached the most awkward time during holidays when I really struggled, for example, to find an activity that appealed to them all, or which they could all participate in.
It has got a lot easier again now as DS1 is nearly 17 so he just does his own thing with his friends anyway, and can easily be left home alone if he doesn't fancy what we're doing. But I won't lie, those kind of 'middle years' were hard.
You'll also most likely be the only one with a young child (or one of very few) once your DS1 is in secondary, for example, and you'll be dealing with completely different educational stages whilst most of your friends will be focused on one. For example I was helping DS3 learn to read whilst supporting DS1 with advanced GCSE preparation and that did feel a bit mad at times.
It's not all about how the siblings will get on, think really hard about the overall logistics and how those will affect your life. Sometimes I do think that DS1 has missed out due to having siblings so much younger. I hope that he will develop more of a relationship with them both once they're grown up, but at the moment I can't say it is really there.
The baby stage is the easy bit (and is lovely, as it's kind of like being a first time mum again but with none of the first time mum stress) but the toddler/preschool years can be tough when you're trying to juggle the needs of a much older child and you can, at times, feel like you're failing everyone.
All that said, though, I wouldn't change any of them now! You clearly really want another baby so I would say go for it. Good luck with the IVF.