Four minutes.
70 feet for 29 minutes puts you in a pressure group "N."
In order to do another dive to 50 feet for 39 minutes, you must be in pressure group "M" prior to making your second dive (see "Table 3 - Repetitive Time Table" at bottom).
To go from pressure group "N" to pressure group "M" requires a surface interval of at least four minutes (and the question specifically asked for the "minimum" amount of time).
Practically speaking, you'd be hard-pressed to get out of the water, change tanks, talk about the first dive, get something to drink, return to the water and begin diving again in four minutes... So the question is really a theoretical question, not a practical one.
Practically speaking, make all of your surface intervals about an hour. It's simple, it's safe, and it gives you time to breathe, talk about the dive, make a new plan for the next dive, fix whatever issue you had on the first dive, etc. You can also change out tanks, get something to drink, warm up, etc...
Also practically speaking, there is no reason whatsoever to run all of your dives so close to the ragged edge of ANY dive table, even one so conservative as the one you're using. You should never need to know whether or not four minutes is going to make or break you. 70 feet for 29 minutes is fine... So is 50 feet for 39 minutes - if you just take the time between the dives to chill and talk and plan the next dive.
Besides, at the end of the day, if you're not running so close to the "ragged edge" - that is, if you take a 1 hour surface interval rather than descending again in a record-breaking four minutes - then you'll end up a lot less tired at the end of the day and have a lot less possibility of dive-related fatigue, even if you didn't actually get bent.
...So the answer to the question is "4 minutes." The answer to the real question is "one hour" - 'cause if you do it that way every time, it's easier to remember, easier to repeat, easier on the body, and physiologically safer. It also gives you time to rest, talk about the first dive, plan the second, tend to your body and gear, and that kind of stuff... Which leads to a much safer dive, too.