Although I have previously done a video on my bobo577 account on youtube on Leviticus 5:11-13, I somewhat deem my initial response to be unsatisfactory, so I thought I might do it here instead.
Firstly, let us deal with the two texts in Hebrews 10:4 and Hebrews 9:22
"10 The law is only a shadow of the good things that are coming—not the realities themselves. For this reason it can never, by the same sacrifices repeated endlessly year after year, make perfect those who draw near to worship. 2 Otherwise, would they not have stopped being offered? For the worshipers would have been cleansed once for all, and would no longer have felt guilty for their sins. 3 But those sacrifices are an annual reminder of sins. 4 It is impossible for the blood of bulls and goats to take away sins.
5 Therefore, when Christ came into the world, he said:
“Sacrifice and offering you did not desire,
but a body you prepared for me;
6 with burnt offerings and sin offerings
you were not pleased.
7 Then I said, ‘Here I am—it is written about me in the scroll—
I have come to do your will, my God.’”[a]
8 First he said, “Sacrifices and offerings, burnt offerings and sin offerings you did not desire, nor were you pleased with them”—though they were offered in accordance with the law. 9 Then he said, “Here I am, I have come to do your will.” He sets aside the first to establish the second. 10 And by that will, we have been made holy through the sacrifice of the body of Jesus Christ once for all."
"9:18 This is why even the first covenant was not put into effect without blood. 19 When Moses had proclaimed every command of the law to all the people, he took the blood of calves, together with water, scarlet wool and branches of hyssop, and sprinkled the scroll and all the people. 20 He said, “This is the blood of the covenant, which God has commanded you to keep.”[e] 21 In the same way, he sprinkled with the blood both the tabernacle and everything used in its ceremonies. 22 In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness."
Both these texts are pitted against each other to try and say that there is a contradiction. However this isn't the case.
In my response to Yisroel Blumenthal, I have mentioned that in Hebrews 10:4, The point the writer is making is the animals were insufficient in taking away sins completely and all they could do is cover a person until the Messiah came to take away their sins, that's all it is saying. The author is saying that Christ's death is a far superior atonement than the animal sacrifices because it actually takes away our sins. The New Testament states that the sacrificial system was replaced by something better or rather fulfilled in Christ.
Now it has been claimed by many such as Rabbi Michael Skobac of Jews for Judaism and Paul Bilal Williams, A Muslim apologist, that Leviticus 5:11-13 refutes Hebrews 9:22, let's take a look:
"11 “‘If, however, they cannot afford two doves or two young pigeons, they are to bring as an offering for their sin a tenth of an ephah[b] of the finest flour for a sin offering. They must not put olive oil or incense on it, because it is a sin offering. 12 They are to bring it to the priest, who shall take a handful of it as a memorial[c] portion and burn it on the altar on top of the food offerings presented to the Lord. It is a sin offering. 13 In this way the priest will make atonement for them for any of these sins they have committed, and they will be forgiven. The rest of the offering will belong to the priest, as in the case of the grain offering.’”"
This text is merely a concession for those who were poor, hence this was only something to carry out in extreme circumstances, it doesn't override the general or overall principle that blood was required. Jamieson-Fausset Brown has made the following point regarding this issue:
"22. almost—to be joined with "all things," namely almost all things under the old dispensation. The exceptions to all things being purified by blood are, Ex 19:10; Le 15:5, &c.; 16:26, 28; 22:6; Nu 31:22-24.
without—Greek, "apart from."
shedding of blood—shed in the slaughter of the victim, and poured out at the altar subsequently. The pouring out of the blood on the altar is the main part of the sacrifice (Le 17:11), and it could not have place apart from the previous shedding of the blood in the slaying. Paul has, perhaps, in mind here, Lu 22:20, "This cup is the new testament in my blood, which is shed for you."
is—Greek, "takes place": comes to pass.
remission—of sins: a favorite expression of Luke, Paul's companion. Properly used of remitting a debt (Mt 6:12; 18:27, 32); our sins are debts. On the truth here, compare Le 5:11-13, an exception because of poverty, confirming the general rule."
Now I am familiar with the answer given by Michael Brown when this text has been raised to him by the Rabbinic Camps, but the text doesn't give even implicit support to what Brown has stated regarding the text, leading me to reject his assertion to find a more biblical conclusion.
Check my words with the scriptures and I hope this article has been a blessing.