〜ようがない
there's no way to
Verb ます-stem + ようがない / ようもない
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ようがない says there's no method or means to do something: 連絡先がわからないので、連絡しようがない, "I don't have their details, so there's no way to contact them". よう here means "way, method", related to 方 (N4).
It attaches to the ます-stem: 直しようがない, 説明しようがない. The reason is usually a missing piece of information or an impossible situation, not a lack of skill.
ようもない is a slightly stronger version. The set phrase どうしようもない means "hopeless, nothing can be done".
Compare the potential negative (直せない), which is about ability. ようがない says the means simply don't exist.
Examples
連絡先がわからないので、連絡しようがない。
I don't have their details, so there's no way to contact them.
こんなに壊れていては、直しようがない。
It's so badly broken that there's no way to fix it.
言葉では説明しようがない。
There's no way to explain it in words.
住所がわからないと、届けようがない。
Without the address, there's no way to deliver it.
今さら謝りようもない。
It's far too late even to apologise now.