Determine single-digit values of M for which the products M*5 end in 5. They are M={1,3,5,7, ...}. Note, for example, that 7*M5 ends in 5, the last digit of 385. Even values of M (as in {2,4,6,8,...} do not have products that end in 5, and thus must be eliminated.
Next, note that if N=5, then M*5 becomes 75, and that 75 multiplied by 5 comes out to 385, which is the desired product.
Noting that L times N*5 (that is, L times 55) = 385, L has to be the same as M, and is in fact 7. Then L times N*5 comes out to 385.
In summary: N=5, M=7 and L=7.