I am adding additional recessed lighting to an existing set of three. The jump in cable length to the additional set will upward of 25' because of running around existing floor joists with out cutting into ceiling. Is this length OK? Safe?

I threw some numbers in the Southwire calculator. Figuring 5 amps load
Voltage drop: 0.63
Voltage drop percentage: 0.53%
Voltage at the end: 119.37

This is new, not added but unless you are adding a large number of high wattage bulbs, you should be OK. Use LCD bulbs and you won't have any issues for sure.

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Wire Material	Copper
Wire Size	14AWG
Voltage	120
Phase	AC single phase
Number of conductors	single set of conductors
Distance*	feet 25
Load current	Amps 5

The cable size you must use depends on the size of the circuit breaker or fuse supplying this branch circuit...
If the circuit breaker is a 15 ampere then #14 AWG is acceptable, if the circuit breaker is 20 ampere then you must use #12 AWG cable.

ma0641 meant to say LED, Not LCD, Good info.

WHAT! No LCD lightbulbs?? Good catch! Thanks. BTW, Lowe's had 60 watt equivalent LED bulbs on Black Friday for 89 cents.