I replaced the bulb in the first two of those 5 also, turned the power back on, and quickly found out I was no longer doing any good.

I'd replace the rest of the bulbs. That will eliminate bulbs as a problem.

Then if those lights still don't work, I'd suspect a break in the line between the last working light and the first non-working light in the string.

But if the last few lights start working, then I'd suspect a problem with the two fixtures that don't work. They may have lost their connection with the electric line, or there may be some other internal issue inside the housing.

--Peter