Bradman's won't be broken.
You'd have to be phenominally consistent over 5 Tests, which is a lot harder than doing it over 3 Tests. I think Cook's series in Australia has made me appreciate just what exactly is involved in scoring 700+ runs in a series, and it's extremely difficult to do.
The problem with that record is their are not enough 5 test series these days except the Ashes ,though it may change in the future.
Yes it requires consistency but i can see it being broken in the future .
I am pretty sure had that series in Srilanka been 5 tests Lara would have come in striking distance given the form he was in.
Not only him even Graham Gooch got 752 runs in a 3 test series against India in 1990.
He just needed 223 runs more in 2 tests to brake it.
It would have been probably broken by now had there been more 5 test series between all teams.
As for Tendulkar's record, there's no reason why Cook can't break it. Looking at their records between their debut and their 26th birthdays, Tendulkar scored 5,177 runs to Cook's 4,859. That's not a huge difference, and I'll wager that Cook will play a lot more Test cricket in the next 10 years than Tendulkar did in the equivelant 10 years of his career.
Like I said, Cook doesn't actually have to improve a great deal from the 45 averaging batsmen he's been so far. If he kicks on for a career average of 50, he'll easily reach 15,000 IMO.
Sachin hasn't actually retired yet though and can see him getting a few more runs yet.
Besides if as you said that being consistent over 5 tests is difficult,being consistent over 15 or 16 years or whatever it will take to break the record is even more tough.
Not only will Cook have to play on till 35/36 he would have to be selected for all England tests ,not have a dip in form or any major injury.
Plus the intensity of test matches played and tests England play will have to remain same and he will most likely have to break the most tests played record too.
I think that record is breakable but can't see Cook being able to mantain his position so long to be able to do it himself.