Naw, 5 weeks is OK, just look at it this way.
When I was born, due date was determined by guessing when the "lucky night" was and adding nine months. This was rather difficult for people with vigorous sex lives. So the calculation has been changed. <irony> For Science! </irony>
Now, you add nine months to the date of the first missed period. OK, so when we compare these two methods, we see that there's about three weeks slop. And a baby being a week early or late is completely unremarkable. All babies in my ancestry have been born about two weeks late for at least three generations, according to first-person accounts gathered by yours truly. Old method of calculation, obviously, but the number of babies born nine months and about two weeks after the wedding night is pretty telling, and there's a couple other reasonable stories too, involving soldiers on leave &etc.
My former cow-orker Barry was born four weeks late, old calculation, and weighed ten pounds at birth. The last time I spoke to him, his mother was still reasonably healthy for somebody 90+ years old. So while I'm sure it can get mighty uncomfortable (like carrying a bowling ball between your knees, I'm told) it's not necessarily a problem. With no other indicators than missing a fairly arbitrary date, the best option is to just wait. Which is not what the doctors will tell you, but it's what my reading of the data says.