Still he could've called/texted/emailed her in those 5 days. Let her know he arrived safely, keep her up to date as to when he's coming back, etc. This is what regular people in relationships do, and even if this is just a contrived TV relationship it's still courteous to do that.
International calling and messaging is costly. He doesn't have voicemail. It is not a real marriage. He owes her nothing. People on this show probably wouldn't be smart enough to access voicemail anyway, ha ha.