05AB1E, 6 bytes

∞-γ€gZ

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Thanks to @Kevin Cruijssen for -1 byte

Code:

∞       push endless list [1, 2, 3, 4, 5, ...]
-       subtract that from input
γ       group by equal elements
€g      push lengths of each group
Z       push max length
        implicitly print top of stack

05AB1E, 7 6 bytes

∞-γ€gZ

Try it online!

Thanks to @Kevin Cruijssen for -1 byte

Code:

∞       push endless list [1, 2, 3, 4, 5, ...]
-       subtract that from input
γ       group by equal elements
€g      push lengths of each group
Z       push max length
        implicitly print top of stack

05AB1E, 7 bytes

TL-γ€gM

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Code:

TL      push [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
-       subtract that from input
γ       group by equal elements
€g      push lengths of each group
M       push max length
        implicitly print top of stack

05AB1E, 6 bytes

∞-γ€gZ

Try it online!

Thanks to @Kevin Cruijssen for -1 byte

Code:

∞       push endless list [1, 2, 3, 4, 5, ...]
-       subtract that from input
γ       group by equal elements
€g      push lengths of each group
Z       push max length
        implicitly print top of stack