Hi,
I don't want to offend you with basic stuff as I know you are an IC designer but maybe one of the links will help to solve the puzzle... The links talk about slew rate formula and also include calculators, and the other two about calculating bandwidth, perhaps
Op-Amp Gain Bandwidth Product is a good one to check first - look about halfway down and after this: '
GBP = ACL x fCL', read the third paragraph (it's pretty close to what you are calculating, I believe): '
For example, with a required gain of 40dB (100), if the op-amp needs to be operated at 100 kHz, then the Gain Bandwidth Product of the op-amp should be at least 100 x 10^5 = 10^7 = 10 MHz.'
From my experiences of learning to select op amps and making the typical beginner mistake again and again of thinking advertised GBW of 1 MHz means the OA can be used at 1 MHz, but then the datasheet shows it's actually more like 50 kHz or (much) worse, I have my rough rule-of-thumb that GBW needs to be about at least 50 to 100 times greater than the frequency applied.
I also did an idiotic calculation of 1/100 kHz = 10us, and without factoring in your gain of 70dB, that would mean it could process a maximum of 10 kHz/us signals, which must be too slow for your needs, and really dodgy calculation was (1us as slew rate is usually V/us) 5mV/1us = 5,000 (whatever that might mean) - as neither of those are 'scientific' maths and I'm an ignoramus I'm sure they are numbers that are not much use to consider and your waste mental energy on exploring further.
One more thing, I'm not totally sure what 'constant gm' means, but I bet you do, and I wondered if an OA that will see a varying input frequency would by necessity require a constant gain block, no doubt your design already has that and I'm just showing my utter ignorance of IC design, again...
An Op Amp Gain Bandwidth Product
Slew Rate Calculator (and formula)
Op Amp Slew Rate Calculator and Formula