They surpassed the 2012 calendar's previous best, achieved at the Monaco Grand Prix, in which di Resta had finished seventh and Hulkenberg was eighth.
Hulkenberg, who collected 10 points today, improved upon his earlier eighth-place finish in Monaco while di Resta, who got six points, finished sixth at the Bahrain leg.
Sahara Force India are now in eighth place on the constructors' table with 44 points.
"A great result for everyone in the team and for me. Fifth place is a great achievement after a long and difficult race. The two-stop strategy worked well, but the last stint was very long and it was hard to hold off the cars behind me on fresher tyres in the last few laps," Hulkenberg said.
Hulkenberg, who started eighth on the grid, gained three places to end the race 19.993 seconds behind winner Fernando Alonso of Ferrari who clocked one hour 44 minutes and 16.649 seconds.
Alonso came home first ahead of Kimi Raikkonen of Lotus and third-placed seven-time champion Michael Schumacher, 43, of Mercedes.
Di Resta, who also gained three places after starting at 10th, was 22.866 seconds behind his Force India team-mate at the Valencia street circuit, which is notoriously tough for overtaking.
"We went very aggressive by only stopping once and in fact we were the only car to pull off this strategy. Of course, when you're stopping once you don't want a safety car period and it cost me some track position," di Resta said.
"But with the way the race unfolded we can't be too disappointed to finish seventh and it's great to have another two-car points finish," he added.
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