My experience with this (and a 7 and 5 year old child) is that you should not let the child win, but rather adjust the scenario so that the child can win. This ensures there is still a sense of accomplishment in the win, and still requires the child to challenge themselves.
I run with my older son from time to time, and as a fairly fast runner myself I certainly am not going to lose a race to him when I try my best (at least, for now). But he enjoys running races; he's much more interested in that than in just running for fun.
So what we do is I give him a head start. We run a block, say, and I know I'm about 5 seconds faster than him normally; so I give him a head start of 5 seconds. I count out loud, and at 5 seconds I take off. Sometimes I win, sometimes he wins; if I win, I adjust the time up a second the next block, and if he wins I adjust the time down a second.
This not only means we have exciting finishes most of the time, but it gives him something else to compete against: he competes to get the head start as low as possible.
You can do a very similar thing in chess. Start by removing your queen from the board, and then play the game as normal. If you still win, remove a rook or a bishop. Find the handicap that works best for her level, where she sometimes wins. Then, experiment by adding back a piece when she starts winning more often.
The game then has two separate goals: winning the individual game (which she can do), and trying to reduce the handicap. You could even set up an ELO-like system; perhaps start with 1500, remove 100 every time she loses, add 100 every time she wins, and when it gets over 2000, lower the handicap by one and return her to 1600. (Conversely, if it gets below 1000, raise the handicap by one.)
You can see some discussions on various advantages and disadvantages of the handicap method of teaching chess here:
I don't suggest Time handicaps (also mentioned in some of the above articles) at five, as she's still not quite up to taking advantage of that time. As she gets older this is a great way to play, giving her longer to think than you, as it can encourage her to think more.