If you really want another puppy, I'd still try to hold out until the current dog is at least 9 months, if not, as recommended a year old.
With the 5 month old, you are just now STARTING the tough "teenage" months. Depending on the individual pup, this can last 3 months, or 6 months or a year!
Now it also sounds like you have the advantage of being home a lot, which is huge. It all depends in the end on how resilient you and your partner feel, in terms of handling chaos etc. The addition of another dog won't lesson your work in the sense of the dogs being able to play with each other and tire each other out (true and good... but!)
In fact it will more than double the amount of mayhem in the house. If you have a high tolerance for mayhem, and you have a strong ability to be patient and work with each dog individually on a regular basis, then you can more easily push it in terms of getting another dog sooner.
BUT if you are looking to make your life easier by getting a companion for the first pup, you should let go of that concept, as it won't be true!