Here are simple hints for each problem. Use them when you are stuck.

A - Banned X 2

Hint 1

Think about the conditions when operations are necessary.

Hint 2

Broadly speaking, there are "cases where $5$s are always adjacent" and "cases where pairs that sum to $10$ are always adjacent".

Hint 3

For the latter case, it corresponds to when there are only two types that sum to $10$. By the way, if neither of the conditions shown in Hint 2 applies, are operations necessary?

Editorial: https://atcoder.jp/contests/arc211/editorial/14697

B - Three Sequences

Hint 1

Think about the conditions under which construction is possible using only $0$s.

Hint 2

Think about the conditions under which construction is possible using only $0$s and $1$s.

Hint 3

Try adjusting the length and the order of $0$s and $1$s nicely.

Editorial: https://atcoder.jp/contests/arc211/editorial/14698

C - Forest

Hint 1

If you run-length compress by the presence or absence of trees, how can operations be expressed?

Hint 2

You should be able to find an upper bound for rewards. Is that upper bound achievable?

Hint 3

It might be easier to think about the first operation that makes it impossible to achieve the upper bound.

Editorial: https://atcoder.jp/contests/arc211/editorial/14699

D - Michishirube

Hint 1

Remove bridges nicely.

Hint 2

It seems harder to achieve with fewer edges. Think about cycles.

Hint 3

Construction should be possible for cycles. Although it's strange to call it a tree, let's view the graph consisting of edges pointed to by blue signposts as a "tree". What kind of tree is it?

Hint 4

In other words, what kind of search process yields that "tree"?

Editorial: https://atcoder.jp/contests/arc211/editorial/14700

E - Greedy Takahashi 2

Hint 1

Think about Snuke's optimal strategy when a tree is given.

Hint 2

When a tree is given, ignoring computational complexity, you should be able to construct a sequence bottom-up.

Hint 3

Use a certain technique to reduce the computational complexity.

Hint 4

Taking advantage of the fact that only judgment is needed, choose a relatively easy implementation.

Editorial: https://atcoder.jp/contests/arc211/editorial/14701