Actually it's not as bad as you think it is. I've been playing a bit with these pumps, and see no issues doing 5 ml a time even with long lines.
My slowest pump is doing about 15 ml/min so that'd mean some 20 seconds of running for 5 ml, which is very reasonable. This is done by making the hose inside the pump head thinner so every turn of the rollers pushes out only a fraction of a ml.
The hoses it connects to are thin, <2 mm internal diameter. That's thin enough for watery solutions to not drip out. So your first dose is inaccurate, but as soon as the lines are full they stay full, so every new run of the motor pushes out the expected volume regardless of line volume and (within limits) the height difference the pump has to overcome.