Lisp

(defun p1-process-rules (line)
  (mapcar #'parse-integer (uiop:split-string line :separator "|")))

(defun p1-process-pages (line)
  (mapcar #'parse-integer (uiop:split-string line :separator ",")))

(defun middle (pages)
  (nth (floor (length pages) 2) pages))

(defun check-rule-p (rule pages)
  (let ((p1 (position (car rule) pages))
        (p2 (position (cadr rule) pages)))
    (or (not p1) (not p2) (< p1 p2))))

(defun ordered-p (pages rules)
  (loop for r in rules
        unless (check-rule-p r pages)
          return nil
        finally
           (return t)))

(defun run-p1 (rules-file pages-file) 
  (let ((rules (read-file rules-file #'p1-process-rules))
        (pages (read-file pages-file #'p1-process-pages)))
    (loop for p in pages
          when (ordered-p p rules)
            sum (middle p)
          )))

(defun fix-pages (rules pages)
  (sort pages (lambda (p1 p2) (ordered-p (list p1 p2) rules)) ))

(defun run-p2 (rules-file pages-file) 
  (let ((rules (read-file rules-file #'p1-process-rules))
        (pages (read-file pages-file #'p1-process-pages)))
    (loop for p in pages
          unless (ordered-p p rules)
            sum (middle (fix-pages rules p))
          )))

Uiua

This is the first one that caused me some headache because I didn't read the instructions carefully enough.
I kept trying to create a sorted list for when all available pages were used, which got me stuck in an endless loop.

Another fun part was figuring out to use memberof (∈) instead of find (⌕) in the last line of FindNext. So much time spent on debugging other areas of the code

Run with example input here

FindNext ← ⊙(
  ⊡1⍉,
  ⊃▽(▽¬)⊸∈
  ⊙⊙(⊡0⍉.)
  :⊙(⟜(▽¬∈))
)

# find the order of pages for a given set of rules
FindOrder ← (
  ◴♭.
  []
  ⍢(⊂FindNext|⋅(>1⧻))
  ⊙◌⊂
)

PartOne ← (
  &rs ∞ &fo "input-5.txt"
  ∩°□°⊟⊜□¬⌕"\n\n".
  ⊙(⊜(□⊜⋕≠@,.)≠@\n.↘1)
  ⊜(⊜⋕≠@|.)≠@\n.

  ⊙.
  ¤
  ⊞(◡(°□:)
    ⟜:⊙(°⊟⍉)
    =2+∩∈
    ▽
    FindOrder
    ⊸≍°□:
    ⊙◌
  )
  ≡◇(⊡⌊÷2⧻.)▽♭
  /+
)

PartTwo ← (
  &rs ∞ &fo "input-5.txt"
  ∩°□°⊟⊜□¬⌕"\n\n".
  ⊙(⊜(□⊜⋕≠@,.)≠@\n.↘1)
  ⊜(⊜⋕≠@|.)≠@\n.
  ⊙.
  ⍜¤⊞(
    ◡(°□:)
    ⟜:⊙(°⊟⍉)
    =2+∩∈
    ▽
    FindOrder
    ⊸≍°□:
    ⊟∩□
  )
  ⊙◌
  ⊃(⊡0)(⊡1)⍉
  ≡◇(⊡⌊÷2⧻.)▽¬≡°□
  /+
)

&p "Day 5:"
&pf "Part 1: "
&p PartOne
&pf "Part 2: "
&p PartTwo

Smalltalk

parsing logic is duplicated between the two, and I probably could use part2's logic for part 1, but yeah

part 1

day5p1: in
	| rules pages i j input |

	input := in lines.
	i := input indexOf: ''.
	rules := ((input copyFrom: 1 to: i-1) collect: [:l | (l splitOn: '|') collect: #asInteger]).
	pages := (input copyFrom: i+1 to: input size) collect: [:l | (l splitOn: ',') collect: #asInteger].
	
	^ pages sum: [ :p |
		(rules allSatisfy: [ :rule |
			i := p indexOf: (rule at: 1).
			j := p indexOf: (rule at: 2).
			(i ~= 0 & (j ~= 0)) ifTrue: [ i < j ] ifFalse: [ true ]
		])
			ifTrue: [p at: ((p size / 2) round: 0) ]
			ifFalse: [0].
	]

part 2

day5p2: in
	| rules pages i pnew input |

	input := in lines.
	i := input indexOf: ''.
	rules := ((input copyFrom: 1 to: i-1) collect: [:l | (l splitOn: '|') collect: #asInteger]).
	pages := (input copyFrom: i+1 to: input size) collect: [:l | (l splitOn: ',') collect: #asInteger].
	
	^ pages sum: [ :p |
		pnew := p sorted: [ :x :y | 
			rules anySatisfy: [ :r | (r at: 1) = x and: [ (r at: 2) = y]]
		].
		pnew ~= p
			ifTrue: [ pnew at: ((pnew size / 2) round: 0) ]
			ifFalse: [0].
	]

I've got a "smart" solution and a really dumb one. I'll start with the smart one (incomplete but you can infer). I did four different ways to try to get it faster, less memory, etc.

// this is from a nuget package. My Mathy roommate told me this was a topological sort.
// It's also my preferred, since it'd perform better on larger data sets.
return lines
    .AsParallel()
    .Where(line => !IsInOrder(GetSoonestOccurrences(line), aggregateRules))
    .Sum(line => line.StableOrderTopologicallyBy(
            getDependencies: page =>
                aggregateRules.TryGetValue(page, out var mustPreceed) ? mustPreceed.Intersect(line) : Enumerable.Empty<Page>())
        .Middle()
    );

The dumb solution. These comparisons aren't fully transitive. I can't believe it works.

public static SortedSet<Page> Sort3(Page[] line,
    Dictionary<Page, System.Collections.Generic.HashSet<Page>> rules)
{
    // how the hell is this working?
    var sorted = new SortedSet<Page>(new Sort3Comparer(rules));
    foreach (var page in line)
        sorted.Add(page);
    return sorted;
}

public static Page[] OrderBy(Page[] line, Dictionary<Page, System.Collections.Generic.HashSet<Page>> rules)
{
    return line.OrderBy(identity, new Sort3Comparer(rules)).ToArray();
}

sealed class Sort3Comparer : IComparer<Page>
{
    private readonly Dictionary<Page, System.Collections.Generic.HashSet<Page>> _rules;

    public Sort3Comparer(Dictionary<Page, System.Collections.Generic.HashSet<Page>> rules) => _rules = rules;

    public int Compare(Page x, Page y)
    {
        if (_rules.TryGetValue(x, out var xrules))
        {
            if (xrules.Contains(y))
                return -1;
        }

        if (_rules.TryGetValue(y, out var yrules))
        {
            if (yrules.Contains(x))
                return 1;
        }

        return 0;
    }
}