As with any change in components, you should back off and work up again. One manufacturers magnum primers may only be another's standard primer as far as pressure is concerned. I have read the main difference between magnum and standard primers is the thickness of the primer cup.
Your 5 gr charge of Bullseye is 17% below Alliant's suggested maximum charge with a 155 gr bullet so, IMHO you are good to go.
I'm not Griz44 but I load my 40 S&W with Unique with a 155 start at 7 gr work up to a max of 8 gr. With a 165 start at 6.5 and work up to a max of 7.2 and with a 180 start at 6 and work up to 6.7. I don't like giving out exact load data because what is safe in my gun(s) may not be safe in yours.
edit: Yes I have and will use magnum pistol primers in non magnum loads. I have a shooting buddy that goes to a winter IPSC match in Colorado he uses small rifle primers in his .38 Super race gun for improved ignition in the freezing temperatures.
The person at CCI told him for all but the most critical BENCH REST competitors who a difference of .001" in group size is the difference in winning and losing the regular primers are more accurate than even the best riflemen can hold. Another fellow, who is also Distinguished, won't use anything but bench rest primers for his match loads, claiming he can tell the difference.