Hi there!
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I believe your answer is:
No, it does not have infinite solutions.
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Here’s why:
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[tex]-7+5x=5x+9\\\rule{150}{0.5}\\\\\rightarrow -7 + 5x = 5x + 9\\\\\rightarrow -7 + 5x - 5x = 5x - 5x +9\\\\\rightarrow -7 = 9[/tex]
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The result is a contradiction. It has no real solutions.
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Hope this helps you. I apologize if it’s incorrect.