My honest opinion-- unfortunately, the 5 year combined peds-anesthesia program would not provide a significant benefit prior to a neonatalogy fellowship, for several reasons. Although anesthesia training would be beneficial for any critical care training, with regards to airway experience, etc., the neonatal population is a very focused age group, where spending 2.5 years doing adult anesthesia would offer very little benefit to your practice as a neonataologist. Unlike the PICU, where you will be taking care of infants through adult ages, there is virtually no overlap between the way adults are cared for and neonates are cared for and their physiology. Neonates are just that special. There would be some benefit to doing a peds anesthesia fellowship (an additional 1-2 years) after the five year program, since you would gain experience with neonatal anesthesia, but NICU babies are a very small proportion of our practice, even in a very big academic center with a large NICU. You would have to rationalize an additional three years of training for that benefit. And I always bring up the issue-general peds boards, anesthesia written and oral boards, peds anesthesia boards, and NICU boards.
If your dream is to spend half of your time doing pediatric anesthesia and the other half of your time being a neonatologist, it can be done, but finding the right position as faculty and making them fit together would be a challenge-- I am not personally aware of anyone who has done this. Happy to chat more-- in a nutshell, if you decide neonatology is for you, then I truly believe the best route is a general peds residency followed by neonatology.