It's not a sign that Madrid being afraid of Arsenal. They have faced the same situation many times, but it's pure their coach wanted his players to get more time to rest. However, i think having likely 4 days to take rest is enough.
I also agreed La liga did it right by rejected Madrid's request. it could give nuance they get a special privilege from La liga.
Its looks normally have 4 days taking rest for upcoming match, firstly Madrid will face Alaves at La Liga match tomorrow days and four days later will face Arsenal at second leg match of UEFA Champion League.
Usually La Liga have privilege for their teams participants at Champion League by early schedule domestic league match and have 5 days left for taking rest before Champion League match, but in this time La Liga rejected Madrid's rechedule match during domestic league have few matches left and possibility the opponent teams as Alaves won't reschedule the match.
In other side, Arsenal have advantage have one more days left taking rest than Real Madrid because domestic league match will face Brentford today.
Giving 5 days privilege is only bringing a new conflict between La liga and other club. I know it so well how it's normally take 5 days as a time to prep, train and gain individual focus. However, La liga can't give Madrid 5 days rest because their rival, Barcelona is only getting 3 days to rest. It's kinda unfair when they did it.