Keeping Speed Boost after death?

My Solution: I would add a value when a player joins if they have the speedboost, then a script which activates it when they die

Script 1: The Value Creator

function Joined(plr)
    local sb = Instance.new("BoolValue", game.Workspace)
    sb.Name = plr.Name.."HasSpeedBoost"
    sb.Value = false
end
game.Players.PlayerAdded:connect(Joined)

Script 2: The Touched Speed Giver

local SpeedBoost = script.Parent

local function touched (part) 
    local parent = part.Parent
    if game.Players:GetPlayerFromCharacter(parent)then
        parent.Humanoid.WalkSpeed = parent.Humanoid.WalkSpeed + 5
    game.Workspace:FindFirstChild(parent.Name.."HasSpeedBoost").Value = true
    end
end

SpeedBoost.Touched:connect(touched)

Script 3: The Died Speed Giver (This can be merged with Script 1)

function Joined(plr)
    plr.Character:WaitForChid("Humanoid").Died:connect(function()
        wait(6) -- Default respawn time add 1
        if game.Workspace[plr.Name.."HasSpeedBoost"].Value == true then
            plr.Character:WaitForChild("Humanoid").WalkSpeed = plr.Character:WaitForChild("Humanoid").WalkSpeed + 5
        end
    end)
end
game.Players.PlayerAdded:connect(Joined)

I hope this helped you

The best way I can think of to accomplish this is to store the total speed boost each player should have in a table, and then apply it to the character each timed they spawn.

Overview

First we need to start off by adding every player who joins to an array. In this array, we'll set the key to the player's name and the value to the amount of speed the player should be boosted. We'll also set it up so that every time a character is respawned, the player will be given the speed boost value associated to their name.

local speedBoost = {}

game.Players.PlayerAdded:connect(function(player)
    speedBoost[player] = 0
    player.CharacterAdded:connect(function(character)
        character.Humanoid.WalkSpeed = character.Humanoid.WalkSpeed + speedBoost[player]
    end)
end)

Now we have to set up some kind of communication between this script, and the touched script of all the speed boost blocks in your game. To do this I will use a BindableEvent which allows for communication between two scripts (Can not communicate cross scope, local to server and vice versa. Use a RemoteEvent for this functionality). We'll put this object in the replicated storage so it is easily accessible.

local AddToSpeedBoost = Instance.new("BindableEvent")
AddToSpeedBoost.Name = "AddToSpeedBoost"
AddToSpeedBoost.Parent = game.ReplicatedStorage

AddToSpeedBoost.Event:connect(function(player, boost)
    speedBoost[player] = speedBoost[player] + boost
end

In order to make it so you can only activate it once however, I will use a table that has each player who has touched the brick inserted into it and use a function to search whether or not the player who touched the brick is in the table

local touched = {}

local function PreviouslyTouched(player)
    for _, value in ipairs (touched) do
        if value == player then
            return true
        end
    end
    return false
end

All we have left to do now is write the touched script. I used a very similar one to yours, just modified the placement of the connection line. When you do the check if the player has touched it or not, you can then fire the BindableEvent and it will add to the player's total speed boost.

script.Parent.Touched:connect(function(part)
    local player = game.Players:GetPlayerFromCharacter(part.Parent)
    if player and not PreviouslyTouched(player) then
        game.ReplicatedStorage.AddToSpeedBoost:Fire(player, 5)
        table.insert(touched, player)
    end
end)

You can have as many speed boosts as you want in your game, and it will just add to the total.

Full Scripts

Server Script In Workspace:

local speedBoost = {}
local AddToSpeedBoost = Instance.new("BindableEvent")
AddToSpeedBoost.Name = "AddToSpeedBoost"
AddToSpeedBoost.Parent = game.ReplicatedStorage

game.Players.PlayerAdded:connect(function(player)
    speedBoost[player] = 0
    player.CharacterAdded:connect(function(character)
        character.Humanoid.WalkSpeed = character.Humanoid.WalkSpeed + speedBoost[player]
    end)
end)

AddToSpeedBoost.Event:connect(function(player, boost)
    speedBoost[player] = speedBoost[player] + boost
end

Server Script In Speed Boost Block:

local touched = {}

local function PreviouslyTouched(player)
    for _, value in ipairs (touched) do
        if value == player then
            return true
        end
    end
    return false
end

script.Parent.Touched:connect(function(part)
    local player = game.Players:GetPlayerFromCharacter(part.Parent)
    if player and not PreviouslyTouched(player) then
        game.ReplicatedStorage.AddToSpeedBoost:Fire(player, 5)
        table.insert(touched, player)
    end
end)