Charles Ellicott Commentary Leviticus 5:11

"But if his means suffice not for two turtle-doves, or two young pigeons, then he shall bring his oblation for that wherein he hath sinned, the tenth part of an ephah of fine flour for a sin-offering: he shall put no oil upon it, neither shall he put any frankincense thereon; for it is a sin-offering." — Leviticus 5:11 (ASV)

But if he is not able. —The benign consideration for the poor, and the desire not to penalize them too heavily for their frailties, are here still more shown in the statute before us. If anyone is so impoverished that the offering of two birds would press too heavily upon him, he might bring the tenth part of an ephah of fine flour, a little less than half a gallon.

For it is a sin offering. —That is, because it is a sin offering, and not a Minchah or meat offering , therefore it is to have no oil or frankincense; otherwise, its distinguishing features as such would be destroyed.