I do think YABU a bit at 5 weeks out - yes anything could happen, but you can't really put life on hold for so long, just make sure you can get him back if you need to.
Thought I would tell you my story just to give you a laugh; whatever happens to your DH it won't be this!
DH went away for a long weekend just before my first was due - we live in the ME, weekend was Thur/Fri, DS was due on the Sat. He was supposed to be working at the Baalbeck Festival in Lebanon, Wed-Fri, and as work was not that thick on the ground, I thought 'chance of baby coming in those 3 days, pretty slim, chance of DH grumping around all weekend if I tell him not to go, pretty high' and just made sure he had a ticket that would get him back straight away if anything did happen.
He called on the Wed, all excited, was up in the Baalbeck Valley and it was beautiful, the festival promised to be a fabulous event.
He then called on the Thursday. Israel had started bombing Lebanon, the airport was closed, they were being told to stay put and do nothing - later, they were taken back to Beirut and put into a hotel, from which they could watch what apparently looked a bit like a fireworks display out at sea...
I had my regular OB appointment on the Saturday - he still there, no immediate prospect of getting out. OB said 'we won't examine you internally or do anything else that might move things along'!
Eventually, the sponsor decided that he and his colleague and the only Western (British) manager in their office were to be driven to the Syrian border and flown home from Damascus. They had 3 cars, one each, each car had two armed security guards and they had all sorts of briefings about 'what to do if...' on this drive which apparently wasn't the world's safest at the best of times (this was just a normal international company btw, these were not VIP precautions) - got to the border, were transferred to other cars, there was an explosion at the border 30 minutes after they went through (though I don't think it was a big one) - got to Damascus airport, which was a bit chaotic due to a lot of Beirut flights being rerouted that way - anyway, they arrived here at 3am, I went to the airport to pick up him and the British manager, who came to stay for a night or two (can't remember) until the company sorted him out with a hotel.
One week earlier I had been really pissed off with DH for inviting people round to dinner as I was really tired in the evenings (working full time) and didn't feel like socialising - this Sunday night I was running around in the wee hours making up beds and driving to the airport; what a difference a bit of context makes!
Eventually gave birth the following Thursday!