Broad's bad run isn't five Tests, it's two, maybe three if he doesn't step up tomorrow (or today if they come back on).
If you wanna purely play cricket-by-numbers, then sure he had a poor Ashes. However, he bowled well. He didn't let us down over there and it was a worry when he went down with the sidestrain. Prior to that, he averaged something pretty low against Pakistan.
He does need to step up, and soon. There are very good alternatives available, Finn really bowled well from day three onwards at Lord's, Bresnan is quality. But this thread isn't about whether he should be in the England XI.
He'd walk into the India side. As would Anderson, Tremlett, Finn, Bresnan, Shazhad, Onions etc