Internally compensated opamp for 5V/V or more
The gain of an op-amp is set by the feedback network.
If you have an amplifier compensated for minimum gain of 5 and apply feedback that results in less gain, phase margin will be inadequate and you run the risk of oscillation, especially at unity gain.
For example, the LMH6624 is decompensated so a minimum gain \$|A_V| \ge 10\$ is required for stability. You can see the gain peaking as a result for relatively low magnitude gains that approach the minimum: