That's usual combinatorics, but I always sucked at it

Chance to be dealt a first diamond : 13/52
Chance to be dealt the second one : 12/51
The three other cards don't matter as they can be diamond or whatever

The chance that at least the two first card of your 5 cards hand are 13/52 * 12/51,

But those 2 diamonds can actually appear in any of the 5 spots and the number of possible combinations is (without repetitions) 5*4 / 2 = 10

My result is therefore 10 * 13/52 * 12/51 = 58,82% as settecba said. That seems a bit high at the fist sight, so I might be off the point.

Thanks iopq for posting math problem, but it is true that I don't see a big interest of such calculation while playing