Erm... there's no 5th team.
Spurs finished 4th in the league when Chelsea won the title and finished 6th. Spurs ended up in the Europa League.
So there's only 4 teams in the Champions League; the exception to that was the season after we won it. Back then, it was up to the FA to decide what they wanted to do with the situation - whether they wanted to back the CL winners or the 4th-placed finisher to take the final place in the competition. After much waffling and I suppose lobbying, we ended up getting a place in the early qualifying rounds against TNS, while Everton kept their place in the playoffs which they subsequently wasted...
As a result, this was born:
Rule 1.03 amendment
UEFA amended Rule 1.03to guarantee future European title holders qualification to the next year’s Champions League competition,
at the expense if necessary of a team in the champion's domestic league which preserves the maximum allowed number of entrants per domestic league, and takes away the authority of the national football association to decide which team to nominate in this situation:
The UEFA Champions League title-holder is guaranteed a place in the group stage even if it does not qualify for the competition through its domestic championship.
a) If the title-holder comes from an association entitled to more than one place in the UEFA Champions League and qualifies for the UEFA Cup through its domestic competitions, the lowest-ranked club of the association’s UEFA Champions League representatives is automatically transferred to the UEFA Cup. In this case, the number of places to which the title-holder's national association is entitled in the UEFA Champions League and the UEFA Cup does not change.
b) If the title-holder comes from an association entitled to more than one place in the UEFA Champions League and does not qualify for the UEFA Champions League or UEFA Cup through its domestic competitions, the lowest-ranked club of the association’s UEFA Champions League representatives is automatically transferred to the UEFA Cup. In this case, the national association of the title-holder is entitled to one additional place in the UEFA Cup.
The limitation applied in the Champions League does not apply in the UEFA Cup, whose rules state:
If the UEFA Cup title-holder does not qualify for either the UEFA Champions League or UEFA Cup through its domestic competitions, its participation in the UEFA Cup will not be at the expense of the contingent of its association.