If the user opens the channel, and funds it unilaterally with 1000, the capacity of the channel will be 1000, and the initial balance 1000 (user)/0 (remote).
Two issues to consider.
Liquidity (Can change over lifetime of channel): In this initial state, only the user can send funds, there is 1000 liquidity in one direction only. As payments are made from from user to remote, liquidity in the opposite direction is built up.
Channel capacity (Does not change over lifetime of channel): Even if there were 1000 liquidity from remote to the user resulting after payment(s) from user to remote, there isn't enough capacity to transfer 5000.
In order for the user to receive a 5000 reward described in your scenario, the following are possibilities, assuming no additional user channels:
- The user initially funded a channel to remote with at least 5000 capacity, and has made enough bets (payments) so that their is at least 5000 liquidity from remote to user. The user has essentially gambled away 5000 worth of payments at his point.
- An additional channel* is opened and funded by remote, to achieve the necessary capacity & liquidity to make collect this reward.
*A cynical observer may note that the house always wins, so that this is rarely necessary.
**On-chain transactions are obviously an alternative way to conduct payouts.