Check the ASM CPU as usually this can cause the issues as the ASM causes a lot of CPU, especially if you making many policies that are still in learning mode:
https://support.f5.com/csp/article/K58571155
Carefully read this article:
https://support.f5.com/csp/article/K47045262
Also it could be that it is LTM issue with bad tcp or http profile, so disable the ASM policy and test the website only with LTM load balancing:
https://support.f5.com/csp/article/K03553427
https://support.f5.com/csp/article/K02408315
https://support.f5.com/csp/article/K5379
As a final test if nothing is seem to help do tcpdumps to see if the F5 is introducing the slowness as when you bypass the F5 device you can also also bypass other network devices that are near the F5 device that can cause issues (the switch connected to the F5 device that is after or before the f5 device for example):
https://support.f5.com/csp/article/K411
https://support.f5.com/csp/article/K13637