A can do a piece of work alone in 15 days, while B complete the same piece of work alone in 12 days. If they work on it together for 5 days, then the fraction of the work that will be left is:

LCM of 15 and 12 is 60 which can be assumed as the total work. 

A can do a piece of work alone in 15 days.

Efficiency of A = $$\frac{60}{15}$$ =  4 units/day

while B complete the same piece of work alone in 12 days.

Efficiency of B = $$\frac{60}{12}$$ = 5 units/day

If they work on it together for 5 days.

Work done by both of them together in 5 days = $$5\times(4+5)$$

= $$5\times9$$

=  45 units

Remaining work = 60-45 = 15 units

The fraction of the work that will be left = $$\frac{15}{60}$$

= $$\frac{1}{4}$$