Will a water pump that is capable of putting out 5 feet high water column in a 1/2 inch pvc pipe have any significant trouble with?

that 5 feet height plus 12 feet horizontal pipe?

?2019-05-14T07:53:07Z

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If you have a pump rated for 6m head then it will be able to pump 5m height and along 12m.
However, it's unsure how fast it will pump.
You can calculate velocity from the following equation.

hL = f (L/D)(V^2/2g)
f = 64/Re assuming laminar flow