If I understand you correctly, that you have five tuners total, you're thinking correctly, at least two ports will see splitter losses equivalent to that of an 8-way split (10.5 to 14 dB).
With four or more tuners in the house, you'll likely notice one or two that are not quite as 'sensitive' as the others. You will also have some cable runs that are longer than others. You will want to feed the weaker tuners or longer runs off of the lower loss splitter outputs. Save the high loss ports for the short cable runs and/or the tuners that perform better.
I usually agree with the advice to find a splitter that has exactly the number of ports needed. I have only occasionally seen 6-way splitters offered, I don't remember ever seeing a 5-way. You are right at the point where if the attic does not cause too much attenuation, no amplifier will be needed. But, you will want to avoid the extra loss that an 8-way split would produce on all ports. I would try the install without any amplifier, using not more that two splitters total (a 4-way followed by a 2-way, not the other way around). If you prove the need for amplification, addition of a one-port DA just ahead of the first splitter would be easy. A
Channel master CM-3410 would be my choice. So far as I can tell, all of the CM-341x multi-port DAs use the same 15 dB amplifier, they just incorporate a 2, 4 or 8 way splitter into the design. If it was certain that you would need a DA, I would have suggested a CM-3418 and termination resistors for all unused ports.
Attics are usually extremely hostile to active electronics (like powered amplifiers) due to the high temperature when the sun is out. The life expectancy of the antenna and cable will be fine, but a preamp may not survive the first hot day.
Avoid daisy chain cabling. That's where you cable up to the first tuner, split 2-ways... cable to the next tuner, split 2-ways and so on to the end. The tail end tuners will get far less signal than they would compared to the home run cable arrangement where a separate cable is run from each tuner back to a single distribution point where the splitter(s) would be located.