No, there are two things called GPT-5 (this is classic OpenAI, see also Codex).

There's GPT-5 the system, a new model routing mechanism that is part of their ChatGPT consumer product.

There's also a new model called GPT-5 which is available via their API: https://platform.openai.com/docs/models/gpt-5

(And two other named API models, GPT-5 mini and GPT-5 nano - part of the GPT-5 model family).

AND there's GPT-5 Pro, which isn't available via the API but can be accessed via ChatGPT for $200/month subscribers.