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I have multiple 50’ lengths of 3/8 crane cable (not aircraft cable). 5k capacity turnbuckles aren’t hard to get…..that’s where my cable idea came from.
I suspect that there will be considerably more than 5000# of tension on the cable - there's considerable mechanical
disadvantage in resisting the collapse of an arch (or resisting a flat surface from becoming a negative arch) unless the angles in the framework resisting it is fairly large. This is why the trusses on a bridge are so tall, so that the angles are large.
[caveat - I'm not an engineer, but I understand triangles, that these triangles are barely worth considering triangles for strengthening purposes!]
With a 6" tall triangle under the bridge standing off a tension rod (or cable), and a 9' wide triangle (for an 18' span), because of the really shallow angle formed in that triangle, you'd end up with huge tension on the rod - probably 15x of the downward weight it's supposed to counter.
If you want to counter 5000# using the tension, your 5k turnbuckle would explode.... even 1/2" grade 60 rebar can only be expected to hold 15k tension (gr 60 rebar - 90k psi tension - 1/2" rebar will have ~0.2 sq in). 1" gr 60 rebar would hold about 72k tension, which is what 4800# over the bridge would put on such a system.
With a 12" tall triangle, the tension would multiplier would be about 10x (vs 15x with the 6" triangle) because the angle is larger, and the rod would have accordingly less tension on it.
An 18" triangle gets a 6x multiplier.
The taller the triangle is, the lower the tension multiplier gets; if your bridge was over a canyon and you had a 9' tall triangle so that the cable made a 45* angle to it, holding off deflection would only require about (weight + 40%) tension... but you've got a little creek and you don't want the tension rod/cable to catch stuff that's floating in high water.
