Would this application schedule be effective.....?yes
Apply right after a shower at 5a.m. yes
Then apply it right after another shower before I go to the gym at 5pm yes
However will the shower after I come home from the gym remove its potency?no, as long as you wait 60, preferably 90 minutes (though thats the "to be sure" time) between application and showering. Less than 60 minutes will have some impact on delivery and thus effectivess, though how much will vary- but it will have some impact
Or does the cream penetrate the skin/pores??it does, see above