D&D 5E Attack bonus vs. damage bonus

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What's the formula look like if you're using one of the -5/+10 feats, and where is the break even point in that case?

You mean Sharpshooter?

Take the expected damage without the feat, add 10 and halve the result. Add the roll to hit (the normal one, without the feat). If the result is less than 21, use the feat.

This ignores edge cases.

Mathematical Reason
Let H be the roll to hit without the feat, and D be the expected damage without the feat.
Using the feat is better if (21-H-5)(D+10)/20 > D(21-H)/20
Rearranging algebraically, H + (D+10)/2 < 21

Example
An elf with a Dex of 19 (+4) and a Proficiency Bonus of +3 shoots his longbow at a hobgoblin (AC18). Is it worth using the feat?

Normally, he is +7 to hit/+4 damage with ranged weapons so the roll to hit AC18 is 11 and the expected longbow damage is 4½ + 4 = 8½. We take 8½ add 10 and halve it to get 9¼, then add the 11 to get 20¼. This is less than 21, so he should use the feat (although it's marginal).

If he was shooting at a hobgoblin warlord (AC20), the result would be no, don't use the feat.