Most religious institutes have an advisory cut-off age, although this is often negotiable. Different houses or provinces of the same institute may have different limits, however - for instance, one Benedictine monastery might say 40, and another might say 45. This is because there are degrees of subsidiarity or local decision-making permitted in most institutes. So it’s always worth asking, because these limits may or may not be absolute.
There’s no real definition of what ‘too old’ would be, so there are no clear answers. Some institutes will take people in their sixties, but there are a lot of factors such as health, life experience, training and professional background to take into consideration. In a teaching community, there may be an issue of the expense involved in training someone to teach when they only have a few working years left by the time they’ve finished religious formation; if it’s a contemplative community, the formation itself will ‘train’ the person in prayer.
I entered religious life in my forties, and to be honest I didn’t really expect to be accepted, although I hoped and prayed very hard. I’m in pretty good health, have a relevant professional background for ministry, and had known my community for some time before applying, but I was a little surprised even so. :o
But I would give anyone the same advice: a call to religious life should be based around the nature of the charism of the particular religious family and their way of life and the ministry they offer: it’s best to discern to whom God is directing you, and only then discern how that call may be lived out. For instance, if a person is called to the Carmelite tradition to which I belong, they can express this as a nun, as an active sister, as a friar (ordained or not), as a secular priest enrolled within the third orders of the family, or as a lay person within the same third orders. Or they may simply live out their commitment to the charism as someone who studies and prays within the Carmelite tradition.
This sense of a particular call is very important in determining God’s will for us, but it may not be as simple as I’ve made it sound, obviously - it’s possible to feel a call to monastic life, for instance, without knowing which community is the right one to approach, and so further exploration and discernment is needed. But I believe that it’s not a good idea to begin a discernment based upon the exceptions that are needed for entry to be possible. I don’t think one should enter e.g. a monastery just because they’re willing to take you, but because they are a place to which you feel called and to which you can make a contribution in line with God’s will. Discernment is not an easy process of self-learning to undergo, but it is rewarding and necessary.