How to load and run feature selection on a dataset with 5,000 samples and 500,000 features?
5000 samples and 500,000 is not that big - it all depends how much memory you have. Also remember you can always and always optimize your data format. e.g. if they are float64 - do they need to be ? if they are categorical, how they are encoded ? (one character or a 20 character word?) and such. so Yes, if you can load the data into memory good for you if not here are the suggestions:

if you only and only have 5K samples - you must not use all for feature selection.
you can drop features that have very low variance - in an extreme scenario if the variance of a column is 0 - for sure it is useless.
there is something called feature-screening proposed by Fan et. al from Princeton https://orfe.princeton.edu/abstracts/feature-screening-distance-correlation-learning - in short: you can lower your dimension by using a univariat model and then afterwards use multivariate-feature selection models.