Don't panic!
I know that there have been problems but according to my calculations he should need to get a new prescription: if his usual dose is 20 units, 4 times a day .
20 units, 4 times a day is 80 units (though why 4?, most of us normally have only 3 main meals, this is a possible problem)
80 x14 =1120units
5 pens = 5x300 =1500 units
1500-1120= 380units
He may also lose some insulin with an air dose at each injection.
So he would be down to his last pen and should get a refill in case of mafunction of the only pen.
Edited for terrible grammar,written whilst cooking dinner!
(added, I think that they all contain 300u so that's what I've used, at 250u he would be clearly into the last pen)