You need to zoom on the transient response to better see any overshoots.Here's the transient response
Try a 120ms simulation time with the start at 90ms.
When compensating a circuit I test both the AC response and the transient response after each change so that both are optimized.
Sometimes the AC response will look okay, but the transient response does not.
Below is my transient simulation with R5 removed, but with a resistor added in series with C1 for good response.
That provides a lead-lag compensation which is often useful in stabilizing op amp circuits.
Edit: Forgot to post the sim. Here it is:
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